answer string | difficulty string | family_id string | id string | parameters_json string | question string | question_generator string | release_answer_check string | solution_steps_json string | solver_author_model string | source_commit string | source_file string | source_review_status string | source_verification_json string | spoken_question string | tolerance string | topic string | track string | variant_id string | wrong_methods_json string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
11/13 | Easy | qe_F001 | qe_F001:1 | {"blue": 2, "red": 12} | A bag holds 12 red and 2 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "11"}, {"name": "remaining_total_balls", "value": "13"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds twelve red and two blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 1 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "12/13"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "66/91"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "2/13"}] |
1/2 | Easy | qe_F001 | qe_F001:2 | {"blue": 8, "red": 9} | A bag holds 9 red and 8 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "8"}, {"name": "remaining_total_balls", "value": "16"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds nine red and eight blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 2 | [{"misconceptions": ["forgets_to_decrement_numerator", "inverts_to_complement_probability"], "value": "9/16"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "9/34"}] |
4/9 | Easy | qe_F001 | qe_F001:3 | {"blue": 10, "red": 9} | A bag holds 9 red and 10 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "8"}, {"name": "remaining_total_balls", "value": "18"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds nine red and ten blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 3 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "1/2"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "4/19"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "5/9"}] |
2/7 | Easy | qe_F001 | qe_F001:4 | {"blue": 10, "red": 5} | A bag holds 5 red and 10 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "4"}, {"name": "remaining_total_balls", "value": "14"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds five red and ten blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 4 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "5/14"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "2/21"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "5/7"}] |
1/2 | Easy | qe_F001 | qe_F001:5 | {"blue": 10, "red": 11} | A bag holds 11 red and 10 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "10"}, {"name": "remaining_total_balls", "value": "20"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds eleven red and ten blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 5 | [{"misconceptions": ["forgets_to_decrement_numerator", "inverts_to_complement_probability"], "value": "11/20"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "11/42"}] |
1/2 | Easy | qe_F001 | qe_F001:6 | {"blue": 5, "red": 6} | A bag holds 6 red and 5 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "5"}, {"name": "remaining_total_balls", "value": "10"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds six red and five blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 6 | [{"misconceptions": ["forgets_to_decrement_numerator", "inverts_to_complement_probability"], "value": "3/5"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "3/11"}] |
11/19 | Easy | qe_F001 | qe_F001:7 | {"blue": 8, "red": 12} | A bag holds 12 red and 8 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "11"}, {"name": "remaining_total_balls", "value": "19"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds twelve red and eight blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 7 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "12/19"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "33/95"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "8/19"}] |
1/2 | Easy | qe_F001 | qe_F001:8 | {"blue": 9, "red": 10} | A bag holds 10 red and 9 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "9"}, {"name": "remaining_total_balls", "value": "18"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds ten red and nine blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 8 | [{"misconceptions": ["forgets_to_decrement_numerator", "inverts_to_complement_probability"], "value": "5/9"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "5/19"}] |
2/3 | Easy | qe_F001 | qe_F001:9 | {"blue": 2, "red": 5} | A bag holds 5 red and 2 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "4"}, {"name": "remaining_total_balls", "value": "6"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds five red and two blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 9 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "5/6"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "10/21"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "1/3"}] |
11/15 | Easy | qe_F001 | qe_F001:10 | {"blue": 4, "red": 12} | A bag holds 12 red and 4 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "11"}, {"name": "remaining_total_balls", "value": "15"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds twelve red and four blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 10 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "4/5"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "11/20"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "4/15"}] |
2/5 | Easy | qe_F001 | qe_F001:11 | {"blue": 6, "red": 5} | A bag holds 5 red and 6 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "4"}, {"name": "remaining_total_balls", "value": "10"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds five red and six blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 11 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "1/2"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "2/11"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "3/5"}] |
1/2 | Easy | qe_F001 | qe_F001:12 | {"blue": 1, "red": 2} | A bag holds 2 red and 1 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "1"}, {"name": "remaining_total_balls", "value": "2"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds two red and one blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 12 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "1"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional", "inverts_to_complement_probability"], "value": "1/3"}] |
5/9 | Easy | qe_F001 | qe_F001:13 | {"blue": 8, "red": 11} | A bag holds 11 red and 8 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "10"}, {"name": "remaining_total_balls", "value": "18"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds eleven red and eight blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 13 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "11/18"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "55/171"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "4/9"}] |
5/6 | Easy | qe_F001 | qe_F001:14 | {"blue": 2, "red": 11} | A bag holds 11 red and 2 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "10"}, {"name": "remaining_total_balls", "value": "12"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds eleven red and two blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 14 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "11/12"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "55/78"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "1/6"}] |
7/8 | Easy | qe_F001 | qe_F001:15 | {"blue": 1, "red": 8} | A bag holds 8 red and 1 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "7"}, {"name": "remaining_total_balls", "value": "8"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds eight red and one blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 15 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "1"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "7/9"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "1/8"}] |
5/6 | Easy | qe_F001 | qe_F001:16 | {"blue": 1, "red": 6} | A bag holds 6 red and 1 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "5"}, {"name": "remaining_total_balls", "value": "6"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds six red and one blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 16 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "1"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "5/7"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "1/6"}] |
9/16 | Easy | qe_F001 | qe_F001:17 | {"blue": 7, "red": 10} | A bag holds 10 red and 7 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "9"}, {"name": "remaining_total_balls", "value": "16"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds ten red and seven blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 17 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "5/8"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "45/136"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "7/16"}] |
5/11 | Easy | qe_F001 | qe_F001:18 | {"blue": 6, "red": 6} | A bag holds 6 red and 6 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "5"}, {"name": "remaining_total_balls", "value": "11"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds six red and six blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 18 | [{"misconceptions": ["forgets_to_decrement_numerator", "inverts_to_complement_probability"], "value": "6/11"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "5/22"}] |
3/5 | Easy | qe_F001 | qe_F001:19 | {"blue": 6, "red": 10} | A bag holds 10 red and 6 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "9"}, {"name": "remaining_total_balls", "value": "15"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds ten red and six blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 19 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "2/3"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "3/8"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "2/5"}] |
1/7 | Easy | qe_F001 | qe_F001:20 | {"blue": 6, "red": 2} | A bag holds 2 red and 6 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "1"}, {"name": "remaining_total_balls", "value": "7"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds two red and six blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 20 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "2/7"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "1/28"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "6/7"}] |
6/11 | Easy | qe_F001 | qe_F001:21 | {"blue": 5, "red": 7} | A bag holds 7 red and 5 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "6"}, {"name": "remaining_total_balls", "value": "11"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds seven red and five blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 21 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "7/11"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "7/22"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "5/11"}] |
11/17 | Easy | qe_F001 | qe_F001:22 | {"blue": 6, "red": 12} | A bag holds 12 red and 6 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "11"}, {"name": "remaining_total_balls", "value": "17"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds twelve red and six blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 22 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "12/17"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "22/51"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "6/17"}] |
7/12 | Easy | qe_F001 | qe_F001:23 | {"blue": 5, "red": 8} | A bag holds 8 red and 5 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "7"}, {"name": "remaining_total_balls", "value": "12"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds eight red and five blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 23 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "2/3"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "14/39"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "5/12"}] |
1/2 | Easy | qe_F001 | qe_F001:24 | {"blue": 2, "red": 3} | A bag holds 3 red and 2 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "2"}, {"name": "remaining_total_balls", "value": "4"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds three red and two blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 24 | [{"misconceptions": ["forgets_to_decrement_numerator", "inverts_to_complement_probability"], "value": "3/4"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "3/10"}] |
9/14 | Easy | qe_F001 | qe_F001:25 | {"blue": 5, "red": 10} | A bag holds 10 red and 5 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "9"}, {"name": "remaining_total_balls", "value": "14"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds ten red and five blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 25 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "5/7"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "3/7"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "5/14"}] |
7/16 | Easy | qe_F001 | qe_F001:26 | {"blue": 9, "red": 8} | A bag holds 8 red and 9 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "7"}, {"name": "remaining_total_balls", "value": "16"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds eight red and nine blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 26 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "1/2"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "7/34"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "9/16"}] |
1/3 | Easy | qe_F001 | qe_F001:27 | {"blue": 2, "red": 2} | A bag holds 2 red and 2 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "1"}, {"name": "remaining_total_balls", "value": "3"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds two red and two blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 27 | [{"misconceptions": ["forgets_to_decrement_numerator", "inverts_to_complement_probability"], "value": "2/3"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "1/6"}] |
3/7 | Easy | qe_F001 | qe_F001:28 | {"blue": 4, "red": 4} | A bag holds 4 red and 4 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "3"}, {"name": "remaining_total_balls", "value": "7"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds four red and four blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 28 | [{"misconceptions": ["forgets_to_decrement_numerator", "inverts_to_complement_probability"], "value": "4/7"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "3/14"}] |
8/13 | Easy | qe_F001 | qe_F001:29 | {"blue": 5, "red": 9} | A bag holds 9 red and 5 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "8"}, {"name": "remaining_total_balls", "value": "13"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds nine red and five blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 29 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "9/13"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "36/91"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "5/13"}] |
4/7 | Easy | qe_F001 | qe_F001:30 | {"blue": 3, "red": 5} | A bag holds 5 red and 3 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "4"}, {"name": "remaining_total_balls", "value": "7"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds five red and three blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 30 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "5/7"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "5/14"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "3/7"}] |
1/2 | Easy | qe_F001 | qe_F001:31 | {"blue": 6, "red": 7} | A bag holds 7 red and 6 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "6"}, {"name": "remaining_total_balls", "value": "12"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds seven red and six blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 31 | [{"misconceptions": ["forgets_to_decrement_numerator", "inverts_to_complement_probability"], "value": "7/12"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "7/26"}] |
9/13 | Easy | qe_F001 | qe_F001:32 | {"blue": 4, "red": 10} | A bag holds 10 red and 4 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "9"}, {"name": "remaining_total_balls", "value": "13"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds ten red and four blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 32 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "10/13"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "45/91"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "4/13"}] |
3/5 | Easy | qe_F001 | qe_F001:33 | {"blue": 2, "red": 4} | A bag holds 4 red and 2 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "3"}, {"name": "remaining_total_balls", "value": "5"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds four red and two blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 33 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "4/5"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional", "inverts_to_complement_probability"], "value": "2/5"}] |
4/5 | Easy | qe_F001 | qe_F001:34 | {"blue": 2, "red": 9} | A bag holds 9 red and 2 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "8"}, {"name": "remaining_total_balls", "value": "10"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds nine red and two blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 34 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "9/10"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "36/55"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "1/5"}] |
9/17 | Easy | qe_F001 | qe_F001:35 | {"blue": 8, "red": 10} | A bag holds 10 red and 8 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "9"}, {"name": "remaining_total_balls", "value": "17"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds ten red and eight blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 35 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "10/17"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "5/17"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "8/17"}] |
7/9 | Easy | qe_F001 | qe_F001:36 | {"blue": 2, "red": 8} | A bag holds 8 red and 2 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "7"}, {"name": "remaining_total_balls", "value": "9"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds eight red and two blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 36 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "8/9"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "28/45"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "2/9"}] |
1/11 | Easy | qe_F001 | qe_F001:37 | {"blue": 10, "red": 2} | A bag holds 2 red and 10 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "1"}, {"name": "remaining_total_balls", "value": "11"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds two red and ten blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 37 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "2/11"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "1/66"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "10/11"}] |
2/3 | Easy | qe_F001 | qe_F001:38 | {"blue": 5, "red": 11} | A bag holds 11 red and 5 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "10"}, {"name": "remaining_total_balls", "value": "15"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds eleven red and five blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 38 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "11/15"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "11/24"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "1/3"}] |
5/12 | Easy | qe_F001 | qe_F001:39 | {"blue": 7, "red": 6} | A bag holds 6 red and 7 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "5"}, {"name": "remaining_total_balls", "value": "12"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds six red and seven blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 39 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "1/2"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "5/26"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "7/12"}] |
11/16 | Easy | qe_F001 | qe_F001:40 | {"blue": 5, "red": 12} | A bag holds 12 red and 5 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "11"}, {"name": "remaining_total_balls", "value": "16"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds twelve red and five blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 40 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "3/4"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "33/68"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "5/16"}] |
8/9 | Easy | qe_F001 | qe_F001:41 | {"blue": 1, "red": 9} | A bag holds 9 red and 1 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "8"}, {"name": "remaining_total_balls", "value": "9"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds nine red and one blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 41 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "1"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "4/5"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "1/9"}] |
7/17 | Easy | qe_F001 | qe_F001:42 | {"blue": 10, "red": 8} | A bag holds 8 red and 10 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "7"}, {"name": "remaining_total_balls", "value": "17"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds eight red and ten blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 42 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "8/17"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "28/153"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "10/17"}] |
2/9 | Easy | qe_F001 | qe_F001:43 | {"blue": 7, "red": 3} | A bag holds 3 red and 7 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "2"}, {"name": "remaining_total_balls", "value": "9"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds three red and seven blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 43 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "1/3"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "1/15"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "7/9"}] |
5/8 | Easy | qe_F001 | qe_F001:44 | {"blue": 3, "red": 6} | A bag holds 6 red and 3 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "5"}, {"name": "remaining_total_balls", "value": "8"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds six red and three blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 44 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "3/4"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "5/12"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "3/8"}] |
2/3 | Easy | qe_F001 | qe_F001:45 | {"blue": 3, "red": 7} | A bag holds 7 red and 3 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "6"}, {"name": "remaining_total_balls", "value": "9"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds seven red and three blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 45 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "7/9"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "7/15"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "1/3"}] |
3/5 | Easy | qe_F001 | qe_F001:46 | {"blue": 4, "red": 7} | A bag holds 7 red and 4 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "6"}, {"name": "remaining_total_balls", "value": "10"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds seven red and four blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 46 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "7/10"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "21/55"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "2/5"}] |
2/7 | Easy | qe_F001 | qe_F001:47 | {"blue": 5, "red": 3} | A bag holds 3 red and 5 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "2"}, {"name": "remaining_total_balls", "value": "7"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds three red and five blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 47 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "3/7"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "3/28"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "5/7"}] |
10/11 | Easy | qe_F001 | qe_F001:48 | {"blue": 1, "red": 11} | A bag holds 11 red and 1 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "10"}, {"name": "remaining_total_balls", "value": "11"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds eleven red and one blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 48 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "1"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "5/6"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "1/11"}] |
5/13 | Easy | qe_F001 | qe_F001:49 | {"blue": 8, "red": 6} | A bag holds 6 red and 8 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "5"}, {"name": "remaining_total_balls", "value": "13"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds six red and eight blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 49 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "6/13"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "15/91"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "8/13"}] |
1/8 | Easy | qe_F001 | qe_F001:50 | {"blue": 7, "red": 2} | A bag holds 2 red and 7 blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "remaining_red_balls", "value": "1"}, {"name": "remaining_total_balls", "value": "8"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F001.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | A bag holds two red and seven blue balls. You draw two without replacement. Given the first ball is red, what is the probability the second is also red? | 0 | Conditional probability | quant | 50 | [{"misconceptions": ["forgets_to_decrement_numerator"], "value": "1/4"}, {"misconceptions": ["computes_unconditional_joint_instead_of_conditional"], "value": "1/36"}, {"misconceptions": ["inverts_to_complement_probability"], "value": "7/8"}] |
3/32 | Easy | qe_F004 | qe_F004:1 | {"faces": 8, "sum": 7} | Two fair dice each have faces 1 to 8. What is the probability their sum is exactly 7? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "64"}, {"name": "favorable_pairs", "value": "6"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eight. What is the probability their sum is exactly seven? | 0 | Discrete probability | quant | 1 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "3/64"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/12"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "3/4"}] |
5/121 | Easy | qe_F004 | qe_F004:2 | {"faces": 11, "sum": 18} | Two fair dice each have faces 1 to 11. What is the probability their sum is exactly 18? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "121"}, {"name": "favorable_pairs", "value": "5"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eleven. What is the probability their sum is exactly eighteen? | 0 | Discrete probability | quant | 2 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "3/121"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/22"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "5/11"}] |
8/81 | Easy | qe_F004 | qe_F004:3 | {"faces": 9, "sum": 11} | Two fair dice each have faces 1 to 9. What is the probability their sum is exactly 11? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "81"}, {"name": "favorable_pairs", "value": "8"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to nine. What is the probability their sum is exactly eleven? | 0 | Discrete probability | quant | 3 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "4/81"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "4/45"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "8/9"}] |
2/81 | Easy | qe_F004 | qe_F004:4 | {"faces": 9, "sum": 3} | Two fair dice each have faces 1 to 9. What is the probability their sum is exactly 3? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "81"}, {"name": "favorable_pairs", "value": "2"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to nine. What is the probability their sum is exactly three? | 0 | Discrete probability | quant | 4 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/81"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/45"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "2/9"}] |
2/27 | Easy | qe_F004 | qe_F004:5 | {"faces": 9, "sum": 7} | Two fair dice each have faces 1 to 9. What is the probability their sum is exactly 7? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "81"}, {"name": "favorable_pairs", "value": "6"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to nine. What is the probability their sum is exactly seven? | 0 | Discrete probability | quant | 5 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/27"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/15"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "2/3"}] |
3/25 | Easy | qe_F004 | qe_F004:6 | {"faces": 5, "sum": 4} | Two fair dice each have faces 1 to 5. What is the probability their sum is exactly 4? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "25"}, {"name": "favorable_pairs", "value": "3"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to five. What is the probability their sum is exactly four? | 0 | Discrete probability | quant | 6 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "2/25"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/15"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "3/5"}] |
4/81 | Easy | qe_F004 | qe_F004:7 | {"faces": 9, "sum": 5} | Two fair dice each have faces 1 to 9. What is the probability their sum is exactly 5? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "81"}, {"name": "favorable_pairs", "value": "4"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to nine. What is the probability their sum is exactly five? | 0 | Discrete probability | quant | 7 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "2/81"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/45"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "4/9"}] |
4/25 | Easy | qe_F004 | qe_F004:8 | {"faces": 5, "sum": 5} | Two fair dice each have faces 1 to 5. What is the probability their sum is exactly 5? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "25"}, {"name": "favorable_pairs", "value": "4"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to five. What is the probability their sum is exactly five? | 0 | Discrete probability | quant | 8 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "2/25"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/15"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "4/5"}] |
1/50 | Easy | qe_F004 | qe_F004:9 | {"faces": 10, "sum": 3} | Two fair dice each have faces 1 to 10. What is the probability their sum is exactly 3? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "100"}, {"name": "favorable_pairs", "value": "2"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to ten. What is the probability their sum is exactly three? | 0 | Discrete probability | quant | 9 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/100"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/55"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "1/5"}] |
2/49 | Easy | qe_F004 | qe_F004:10 | {"faces": 7, "sum": 13} | Two fair dice each have faces 1 to 7. What is the probability their sum is exactly 13? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "49"}, {"name": "favorable_pairs", "value": "2"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to seven. What is the probability their sum is exactly thirteen? | 0 | Discrete probability | quant | 10 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/49"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/28"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "2/7"}] |
6/49 | Easy | qe_F004 | qe_F004:11 | {"faces": 7, "sum": 7} | Two fair dice each have faces 1 to 7. What is the probability their sum is exactly 7? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "49"}, {"name": "favorable_pairs", "value": "6"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to seven. What is the probability their sum is exactly seven? | 0 | Discrete probability | quant | 11 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "3/49"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "3/28"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "6/7"}] |
1/10 | Easy | qe_F004 | qe_F004:12 | {"faces": 10, "sum": 11} | Two fair dice each have faces 1 to 10. What is the probability their sum is exactly 11? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "100"}, {"name": "favorable_pairs", "value": "10"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to ten. What is the probability their sum is exactly eleven? | 0 | Discrete probability | quant | 12 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/20"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/11"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "1"}] |
7/100 | Easy | qe_F004 | qe_F004:13 | {"faces": 10, "sum": 8} | Two fair dice each have faces 1 to 10. What is the probability their sum is exactly 8? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "100"}, {"name": "favorable_pairs", "value": "7"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to ten. What is the probability their sum is exactly eight? | 0 | Discrete probability | quant | 13 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/25"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "4/55"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "7/10"}] |
2/25 | Easy | qe_F004 | qe_F004:14 | {"faces": 5, "sum": 9} | Two fair dice each have faces 1 to 5. What is the probability their sum is exactly 9? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "25"}, {"name": "favorable_pairs", "value": "2"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to five. What is the probability their sum is exactly nine? | 0 | Discrete probability | quant | 14 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/25"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/15"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "2/5"}] |
7/121 | Easy | qe_F004 | qe_F004:15 | {"faces": 11, "sum": 16} | Two fair dice each have faces 1 to 11. What is the probability their sum is exactly 16? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "121"}, {"name": "favorable_pairs", "value": "7"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eleven. What is the probability their sum is exactly sixteen? | 0 | Discrete probability | quant | 15 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "4/121"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/33"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "7/11"}] |
3/49 | Easy | qe_F004 | qe_F004:16 | {"faces": 7, "sum": 4} | Two fair dice each have faces 1 to 7. What is the probability their sum is exactly 4? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "49"}, {"name": "favorable_pairs", "value": "3"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to seven. What is the probability their sum is exactly four? | 0 | Discrete probability | quant | 16 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "2/49"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/14"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "3/7"}] |
2/27 | Easy | qe_F004 | qe_F004:17 | {"faces": 9, "sum": 13} | Two fair dice each have faces 1 to 9. What is the probability their sum is exactly 13? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "81"}, {"name": "favorable_pairs", "value": "6"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to nine. What is the probability their sum is exactly thirteen? | 0 | Discrete probability | quant | 17 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/27"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/15"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "2/3"}] |
6/121 | Easy | qe_F004 | qe_F004:18 | {"faces": 11, "sum": 7} | Two fair dice each have faces 1 to 11. What is the probability their sum is exactly 7? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "121"}, {"name": "favorable_pairs", "value": "6"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eleven. What is the probability their sum is exactly seven? | 0 | Discrete probability | quant | 18 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "3/121"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/22"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "6/11"}] |
1/72 | Easy | qe_F004 | qe_F004:19 | {"faces": 12, "sum": 23} | Two fair dice each have faces 1 to 12. What is the probability their sum is exactly 23? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "144"}, {"name": "favorable_pairs", "value": "2"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to twelve. What is the probability their sum is exactly twenty-three? | 0 | Discrete probability | quant | 19 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/144"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/78"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "1/6"}] |
7/64 | Easy | qe_F004 | qe_F004:20 | {"faces": 8, "sum": 8} | Two fair dice each have faces 1 to 8. What is the probability their sum is exactly 8? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "64"}, {"name": "favorable_pairs", "value": "7"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eight. What is the probability their sum is exactly eight? | 0 | Discrete probability | quant | 20 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/16"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/9"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "7/8"}] |
1/25 | Easy | qe_F004 | qe_F004:21 | {"faces": 10, "sum": 5} | Two fair dice each have faces 1 to 10. What is the probability their sum is exactly 5? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "100"}, {"name": "favorable_pairs", "value": "4"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to ten. What is the probability their sum is exactly five? | 0 | Discrete probability | quant | 21 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/50"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/55"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "2/5"}] |
11/144 | Easy | qe_F004 | qe_F004:22 | {"faces": 12, "sum": 12} | Two fair dice each have faces 1 to 12. What is the probability their sum is exactly 12? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "144"}, {"name": "favorable_pairs", "value": "11"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to twelve. What is the probability their sum is exactly twelve? | 0 | Discrete probability | quant | 22 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/24"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/13"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "11/12"}] |
7/121 | Easy | qe_F004 | qe_F004:23 | {"faces": 11, "sum": 8} | Two fair dice each have faces 1 to 11. What is the probability their sum is exactly 8? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "121"}, {"name": "favorable_pairs", "value": "7"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eleven. What is the probability their sum is exactly eight? | 0 | Discrete probability | quant | 23 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "4/121"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/33"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "7/11"}] |
1/8 | Easy | qe_F004 | qe_F004:24 | {"faces": 4, "sum": 7} | Two fair dice each have faces 1 to 4. What is the probability their sum is exactly 7? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "16"}, {"name": "favorable_pairs", "value": "2"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to four. What is the probability their sum is exactly seven? | 0 | Discrete probability | quant | 24 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/16"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/10"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "1/2"}] |
7/100 | Easy | qe_F004 | qe_F004:25 | {"faces": 10, "sum": 14} | Two fair dice each have faces 1 to 10. What is the probability their sum is exactly 14? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "100"}, {"name": "favorable_pairs", "value": "7"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to ten. What is the probability their sum is exactly fourteen? | 0 | Discrete probability | quant | 25 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/25"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "4/55"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "7/10"}] |
8/121 | Easy | qe_F004 | qe_F004:26 | {"faces": 11, "sum": 15} | Two fair dice each have faces 1 to 11. What is the probability their sum is exactly 15? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "121"}, {"name": "favorable_pairs", "value": "8"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eleven. What is the probability their sum is exactly fifteen? | 0 | Discrete probability | quant | 26 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "4/121"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/33"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "8/11"}] |
1/24 | Easy | qe_F004 | qe_F004:27 | {"faces": 12, "sum": 7} | Two fair dice each have faces 1 to 12. What is the probability their sum is exactly 7? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "144"}, {"name": "favorable_pairs", "value": "6"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to twelve. What is the probability their sum is exactly seven? | 0 | Discrete probability | quant | 27 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/48"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/26"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "1/2"}] |
1/16 | Easy | qe_F004 | qe_F004:28 | {"faces": 8, "sum": 13} | Two fair dice each have faces 1 to 8. What is the probability their sum is exactly 13? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "64"}, {"name": "favorable_pairs", "value": "4"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eight. What is the probability their sum is exactly thirteen? | 0 | Discrete probability | quant | 28 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/32"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/18"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "1/2"}] |
3/100 | Easy | qe_F004 | qe_F004:29 | {"faces": 10, "sum": 4} | Two fair dice each have faces 1 to 10. What is the probability their sum is exactly 4? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "100"}, {"name": "favorable_pairs", "value": "3"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to ten. What is the probability their sum is exactly four? | 0 | Discrete probability | quant | 29 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/50"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/55"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "3/10"}] |
3/100 | Easy | qe_F004 | qe_F004:30 | {"faces": 10, "sum": 18} | Two fair dice each have faces 1 to 10. What is the probability their sum is exactly 18? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "100"}, {"name": "favorable_pairs", "value": "3"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to ten. What is the probability their sum is exactly eighteen? | 0 | Discrete probability | quant | 30 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/50"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/55"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "3/10"}] |
1/4 | Easy | qe_F004 | qe_F004:31 | {"faces": 4, "sum": 5} | Two fair dice each have faces 1 to 4. What is the probability their sum is exactly 5? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "16"}, {"name": "favorable_pairs", "value": "4"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to four. What is the probability their sum is exactly five? | 0 | Discrete probability | quant | 31 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/8"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/5"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "1"}] |
9/100 | Easy | qe_F004 | qe_F004:32 | {"faces": 10, "sum": 10} | Two fair dice each have faces 1 to 10. What is the probability their sum is exactly 10? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "100"}, {"name": "favorable_pairs", "value": "9"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to ten. What is the probability their sum is exactly ten? | 0 | Discrete probability | quant | 32 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/20"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/11"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "9/10"}] |
8/121 | Easy | qe_F004 | qe_F004:33 | {"faces": 11, "sum": 9} | Two fair dice each have faces 1 to 11. What is the probability their sum is exactly 9? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "121"}, {"name": "favorable_pairs", "value": "8"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eleven. What is the probability their sum is exactly nine? | 0 | Discrete probability | quant | 33 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "4/121"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/33"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "8/11"}] |
3/49 | Easy | qe_F004 | qe_F004:34 | {"faces": 7, "sum": 12} | Two fair dice each have faces 1 to 7. What is the probability their sum is exactly 12? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "49"}, {"name": "favorable_pairs", "value": "3"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to seven. What is the probability their sum is exactly twelve? | 0 | Discrete probability | quant | 34 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "2/49"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/14"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "3/7"}] |
1/32 | Easy | qe_F004 | qe_F004:35 | {"faces": 8, "sum": 3} | Two fair dice each have faces 1 to 8. What is the probability their sum is exactly 3? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "64"}, {"name": "favorable_pairs", "value": "2"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eight. What is the probability their sum is exactly three? | 0 | Discrete probability | quant | 35 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/64"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/36"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "1/4"}] |
1/32 | Easy | qe_F004 | qe_F004:36 | {"faces": 8, "sum": 15} | Two fair dice each have faces 1 to 8. What is the probability their sum is exactly 15? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "64"}, {"name": "favorable_pairs", "value": "2"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eight. What is the probability their sum is exactly fifteen? | 0 | Discrete probability | quant | 36 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/64"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/36"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "1/4"}] |
3/50 | Easy | qe_F004 | qe_F004:37 | {"faces": 10, "sum": 15} | Two fair dice each have faces 1 to 10. What is the probability their sum is exactly 15? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "100"}, {"name": "favorable_pairs", "value": "6"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to ten. What is the probability their sum is exactly fifteen? | 0 | Discrete probability | quant | 37 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "3/100"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "3/55"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "3/5"}] |
6/121 | Easy | qe_F004 | qe_F004:38 | {"faces": 11, "sum": 17} | Two fair dice each have faces 1 to 11. What is the probability their sum is exactly 17? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "121"}, {"name": "favorable_pairs", "value": "6"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eleven. What is the probability their sum is exactly seventeen? | 0 | Discrete probability | quant | 38 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "3/121"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/22"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "6/11"}] |
7/144 | Easy | qe_F004 | qe_F004:39 | {"faces": 12, "sum": 18} | Two fair dice each have faces 1 to 12. What is the probability their sum is exactly 18? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "144"}, {"name": "favorable_pairs", "value": "7"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to twelve. What is the probability their sum is exactly eighteen? | 0 | Discrete probability | quant | 39 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/36"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/39"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "7/12"}] |
7/81 | Easy | qe_F004 | qe_F004:40 | {"faces": 9, "sum": 8} | Two fair dice each have faces 1 to 9. What is the probability their sum is exactly 8? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "81"}, {"name": "favorable_pairs", "value": "7"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to nine. What is the probability their sum is exactly eight? | 0 | Discrete probability | quant | 40 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "4/81"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "4/45"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "7/9"}] |
1/16 | Easy | qe_F004 | qe_F004:41 | {"faces": 12, "sum": 10} | Two fair dice each have faces 1 to 12. What is the probability their sum is exactly 10? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "144"}, {"name": "favorable_pairs", "value": "9"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to twelve. What is the probability their sum is exactly ten? | 0 | Discrete probability | quant | 41 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "5/144"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "5/78"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "3/4"}] |
1/12 | Easy | qe_F004 | qe_F004:42 | {"faces": 6, "sum": 4} | Two fair dice each have faces 1 to 6. What is the probability their sum is exactly 4? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "36"}, {"name": "favorable_pairs", "value": "3"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to six. What is the probability their sum is exactly four? | 0 | Discrete probability | quant | 42 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/18"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/21"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "1/2"}] |
4/25 | Easy | qe_F004 | qe_F004:43 | {"faces": 5, "sum": 7} | Two fair dice each have faces 1 to 5. What is the probability their sum is exactly 7? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "25"}, {"name": "favorable_pairs", "value": "4"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to five. What is the probability their sum is exactly seven? | 0 | Discrete probability | quant | 43 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "2/25"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/15"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "4/5"}] |
5/64 | Easy | qe_F004 | qe_F004:44 | {"faces": 8, "sum": 12} | Two fair dice each have faces 1 to 8. What is the probability their sum is exactly 12? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "64"}, {"name": "favorable_pairs", "value": "5"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to eight. What is the probability their sum is exactly twelve? | 0 | Discrete probability | quant | 44 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "3/64"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/12"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "5/8"}] |
1/18 | Easy | qe_F004 | qe_F004:45 | {"faces": 12, "sum": 9} | Two fair dice each have faces 1 to 12. What is the probability their sum is exactly 9? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "144"}, {"name": "favorable_pairs", "value": "8"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to twelve. What is the probability their sum is exactly nine? | 0 | Discrete probability | quant | 45 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/36"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "2/39"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "2/3"}] |
5/36 | Easy | qe_F004 | qe_F004:46 | {"faces": 6, "sum": 6} | Two fair dice each have faces 1 to 6. What is the probability their sum is exactly 6? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "36"}, {"name": "favorable_pairs", "value": "5"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to six. What is the probability their sum is exactly six? | 0 | Discrete probability | quant | 46 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/12"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/7"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "5/6"}] |
2/81 | Easy | qe_F004 | qe_F004:47 | {"faces": 9, "sum": 17} | Two fair dice each have faces 1 to 9. What is the probability their sum is exactly 17? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "81"}, {"name": "favorable_pairs", "value": "2"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to nine. What is the probability their sum is exactly seventeen? | 0 | Discrete probability | quant | 47 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/81"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/45"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "2/9"}] |
5/144 | Easy | qe_F004 | qe_F004:48 | {"faces": 12, "sum": 6} | Two fair dice each have faces 1 to 12. What is the probability their sum is exactly 6? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "144"}, {"name": "favorable_pairs", "value": "5"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to twelve. What is the probability their sum is exactly six? | 0 | Discrete probability | quant | 48 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/48"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/26"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "5/12"}] |
1/72 | Easy | qe_F004 | qe_F004:49 | {"faces": 12, "sum": 3} | Two fair dice each have faces 1 to 12. What is the probability their sum is exactly 3? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "144"}, {"name": "favorable_pairs", "value": "2"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to twelve. What is the probability their sum is exactly three? | 0 | Discrete probability | quant | 49 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/144"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/78"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "1/6"}] |
1/48 | Easy | qe_F004 | qe_F004:50 | {"faces": 12, "sum": 4} | Two fair dice each have faces 1 to 12. What is the probability their sum is exactly 4? | Claude (project disclosure) | recomputed_exact_from_parameters | [{"name": "total_outcomes", "value": "144"}, {"name": "favorable_pairs", "value": "3"}] | meta-models/muse-spark-open-1026 | 5db4b185d28eeee3fa89082dee6aeeca00bb115e | content/forge/qe_F004.json | pending_builder_review | {"all_variants_retained": true, "method_count": 3, "misconceptions_verified": true, "mode": "imported_verified_families", "pending_reason": null, "reason": null, "rechecked_parameter_revision": null, "repair_attempted": true, "solver": {"max_absolute_error": "0", "passed": true, "variants_checked": 50}, "source": {"pas... | Two fair dice each have faces one to twelve. What is the probability their sum is exactly four? | 0 | Discrete probability | quant | 50 | [{"misconceptions": ["unordered_pairs_over_n_squared"], "value": "1/72"}, {"misconceptions": ["unordered_sample_space_n_choose_2_with_replacement"], "value": "1/39"}, {"misconceptions": ["favorable_over_faces_not_squared"], "value": "1/4"}] |
Unbluffable Numeric Interview Questions
600 model-generated numeric interview-practice questions from 12 parameterised families across quant, investment banking, consulting and software engineering. Each released answer was recomputed from its parameters with exact Python arithmetic by the included release validator.
This is a small reusable question corpus from Unbluffable, a spoken mock interviewer built for the Meta Global AI Developer Hackathon. It contains questions and answer-key metadata. It contains no candidate answers, user recordings, personal data, behavioural interview transcripts or private source question bank.
Content
| Family | Track | Topic | Variants |
|---|---|---|---|
| qe_F001 | quant | Conditional probability | 50 |
| qe_F004 | quant | Discrete probability | 50 |
| qe_F005 | quant | Discrete probability | 50 |
| co_F001 | consulting | Profitability | 50 |
| co_F005 | consulting | Breakeven | 50 |
| co_F008 | consulting | Market sizing with stated assumptions | 50 |
| ib_F002 | investment_banking | Accounting and three-statement linkages | 50 |
| ib_F007 | investment_banking | Enterprise value and equity value bridge | 50 |
| ib_F009 | investment_banking | Valuation multiples | 50 |
| sw_F005 | software_engineering | Sliding window | 50 |
| sw_F020 | software_engineering | Heaps | 50 |
| sw_F024 | software_engineering | Prefix sums | 50 |
All selected families have recorded zero-error solver checks in the source repository and zero declared numeric tolerance. We release every stored variant of these selected families, without changing question wording or answer values.
Provenance
- Public source commit:
5db4b185d28eeee3fa89082dee6aeeca00bb115e. - Source question/variant generation: ChatGPT, except the selected
qe_quant families, written by Claude, according to the project's disclosures. - Original solver author: Muse Spark Open (
meta-models/muse-spark-open-1026) on Baseten. - Original forge verification compared solver output with stored answers across all variants; the original metadata is preserved per row.
- Release validation: the included
validate_dataset.pyimplements the 12 answer formulae and recomputes each answer exactly from its parameters. This validation was prepared with Codex. - Source family files may say
pending_builder_review. Those values are retained insource_review_status; this release does not claim completed human review. - The original source solvers are not bundled. The included validator is a separate release implementation of the selected answer computations.
- MIT license and the original copyright notice are included from the public source repository.
Files and fields
data/questions.jsonl has one JSON object per question variant. IDs use family_id:variant_id. The public source and its file hashes are listed in manifest.json.
| Field | Meaning |
|---|---|
id, family_id, variant_id |
Stable identifiers for this release |
track, topic, difficulty |
Source categories, not independently assessed difficulty |
question, spoken_question |
Original display and spoken question text |
answer |
Exact rational value represented as a string, e.g. 4/5 or 570 |
tolerance |
Zero for every row in this release |
parameters_json |
JSON-encoded parameter object; rational strings retain exact values |
wrong_methods_json |
Retained source wrong-method values and names |
solution_steps_json |
Retained named intermediate values from the source |
question_generator, solver_author_model |
Disclosed generator and recorded solver model |
source_review_status, source_verification_json |
Original review status and machine-check metadata |
release_answer_check |
Exact recomputation performed for the release |
source_file, source_commit |
Pinned public source locations |
Percentage answers, where present in a future extension, require an explicit convention. This version selects questions whose requested units are described in their text; preserve those units when interpreting numeric values.
Load locally
import json
from fractions import Fraction
from pathlib import Path
rows = [json.loads(line) for line in Path("data/questions.jsonl").read_text(encoding="utf-8").splitlines()]
example = rows[0]
print(example["question"], Fraction(example["answer"]))
After cloning or downloading the dataset repository, run:
python validate_dataset.py
This command requires only Python's standard library. It checks IDs, counts, the data checksum, exact numerical answers and wrong-answer collisions. validation_report.json records the release result.
Intended use and limitations
Use this corpus for interview-practice prototypes, exact-answer checker development and exploring parameterised questions. It is not an unseen benchmark: the questions and answers are public, synthetic and grouped into closely related families.
- There is a single
questionscorpus split, with no claim of a held-out test set. Any future training/evaluation split should separate whole families to reduce leakage from related variants. - Exact recomputation establishes agreement with the included formulae. It does not establish unambiguous wording, complete domain realism, or validity of a candidate's reasoning.
- Source wrong-method names and intermediate steps are retained annotations. The release validator checks that wrong values differ from the answer; it does not reproduce every wrong-method algorithm or verify every step annotation.
- The consulting questions here are numerical. Behavioural practice and its reported user experience are outside this dataset.
- The corpus does not measure interview improvement, hiring outcomes or model superiority.
- The selection is deliberately small and Easy-labelled; it is not representative of all interviews or of the full Unbluffable bank.
Version
Version 1.0.0, prepared 4 November 2026. Family selection, source-file SHA-256 hashes and the JSONL checksum are in manifest.json.
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