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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"}]
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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.py implements 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 in source_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 questions corpus 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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