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A museum archive process has hidden states coral, hazel, violet. At each step, it FIRST changes state using the transition table and THEN emits the observed symbol using the new state. This repeats for every observed symbol. Conditional on the hidden state sequence, emissions are independent. State order in every vecto...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Final hidden state violet", "criteria": null }, { "id": "o1", "name": "Final hidden state hazel", "criteria": null }, { "id": "o2", "name": "Final hidden state coral", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.7499091054513536, 0.2031918014879223, 0.046899093060724165 ] }
A system evolves through eight mutually exclusive latent states, labeled outcome_0 through outcome_7. At the initial time step, the probability distribution across these states is as follows: outcome_0 has 12/83, outcome_1 has 13/83, outcome_2 has 8/83, outcome_3 has 15/83, outcome_4 has 6/83, outcome_5 has 4/83, outco...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_4", "criteria": null }, { "id": "o1", "name": "outcome_3", "criteria": null }, { "id": "o2", "name": "outcome_5", "criteria": null }, { "id": "o3", "name": "outcome_0", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.0791567007538376, 0.12184301136839938, 0.0481587121057819, 0.021684889554761246, 0.03587817146239143, 0.5934710365688466, 0.010871843771648905, 0.08893563441433297 ] }
A finite Bayesian model is defined with four mutually exclusive outcomes labeled outcome_0, outcome_1, outcome_2, and outcome_3. The prior probabilities for these outcomes are assigned as follows: outcome_0 has a prior of 41/93, outcome_1 has a prior of 11/31, outcome_2 has a prior of 11/93, and outcome_3 has a prior o...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_0", "criteria": null }, { "id": "o1", "name": "outcome_3", "criteria": null }, { "id": "o2", "name": "outcome_1", "criteria": null }, { "id": "o3", "name": "outcome_2", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.06984667802385008, 0.21805792163543442, 0.4497444633730835, 0.262350936967632 ] }
A astronomy club process has hidden states amber, coral, ivory. At each step, it FIRST changes state using the transition table and THEN emits the observed symbol using the new state. This repeats for every observed symbol. Conditional on the hidden state sequence, emissions are independent. State order in every vector...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Final hidden state coral", "criteria": null }, { "id": "o1", "name": "Final hidden state amber", "criteria": null }, { "id": "o2", "name": "Final hidden state ivory", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.3348072134225996, 0.16079921211626388, 0.5043935744611365 ] }
A public library investigation relies on an exhaustive table of mutually exclusive scenarios. Each scenario is selected with a probability proportional to its assigned integer weight. Witnesses are permitted to share information, and no assumption of independence is made. We have observed exactly the event labeled 'MAT...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Responsible person: Hugo", "criteria": null }, { "id": "o1", "name": "Responsible person: Uma", "criteria": null }, { "id": "o2", "name": "Responsible person: Jules", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.5535714285714286, 0.017857142857142856, 0.42857142857142855 ] }
A astronomy club process has hidden states cobalt, cedar, indigo. At each step, it FIRST changes state using the transition table and THEN emits the observed symbol using the new state. This repeats for every observed symbol. Conditional on the hidden state sequence, emissions are independent. State order in every vect...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Final hidden state cobalt", "criteria": null }, { "id": "o1", "name": "Final hidden state cedar", "criteria": null }, { "id": "o2", "name": "Final hidden state indigo", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.4921125308970835, 0.20342506358957588, 0.30446240551334064 ] }
A field research station receives items from mutually exclusive suppliers. An item first passes a selection filter, then is inspected. Given its supplier, selection and a positive inspection are independent. The observed item was selected AND inspected positive; both pieces of evidence must be conditioned on. Supplier ...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Supplier silver", "criteria": null }, { "id": "o1", "name": "Supplier ochre", "criteria": null }, { "id": "o2", "name": "Supplier cedar", "criteria": null }, { "id": "o3", "name": "Supplier indigo", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.7056907037358818, 0.043440486533449174, 0.07298001737619461, 0.17788879235447436 ] }
An astronomy club dispatcher is tasked with selecting the lowest-cost service from the pool of options that are both eligible and currently available. If no service meets both criteria, no selection is made. Eligibility is fixed and confirmed for all listed services. The availability of each service is an independent e...
What is the probability distribution of the service-selection outcome?
[ { "id": "o0", "name": "No service is selected", "criteria": null }, { "id": "o1", "name": "Select service cobalt", "criteria": null }, { "id": "o2", "name": "Select service ruby", "criteria": null }, { "id": "o3", "name": "Select service indigo", "criteria...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.02205, 0.255, 0.0135, 0.7, 0.00945 ] }
At a field research station, exactly one of the following bins contains a missing item. Two inspectors each produce a positive or negative report. Their reports are conditionally independent given the true bin, not unconditionally independent. Both reports were positive. Bin cobalt: prior 2/13; positive-report probabil...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Item is in bin cobalt", "criteria": null }, { "id": "o1", "name": "Item is in bin ruby", "criteria": null }, { "id": "o2", "name": "Item is in bin ochre", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.026765799256505577, 0.06319702602230483, 0.9100371747211896 ] }
A museum archive process has hidden states violet, cedar, jade. At each step, it FIRST changes state using the transition table and THEN emits the observed symbol using the new state. This repeats for every observed symbol. Conditional on the hidden state sequence, emissions are independent. State order in every vector...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Final hidden state violet", "criteria": null }, { "id": "o1", "name": "Final hidden state jade", "criteria": null }, { "id": "o2", "name": "Final hidden state cedar", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.17341607516536348, 0.0604375799677358, 0.7661463448669007 ] }
一个货运站点的集装箱内装有 14 个标记令牌和 12 个未标记令牌。现从中不放回地均匀随机抽取恰好 2 个令牌。任意由 2 个独立令牌组成的子集被抽中的可能性均相等。
What is the probability of each possible marked-token count?
[ { "id": "o0", "name": "Exactly 0 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 1 marked tokens are drawn", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.20307692307692307, 0.28, 0.5169230769230769 ] }
在一个有限的贝叶斯决策模型中,我们面临三个互斥的结果:outcome_0、outcome_1 和 outcome_2。根据现有记录,这三个结果的先验概率分别为 27/52、23/52 和 1/26。在特定观测条件下,各结果对应的似然度(条件概率)分别为:outcome_0 为 7/20,outcome_1 为 11/20,outcome_2 为 19/20。基于这些固定的数值和依赖关系,需要确定在给定观测下,这三个互斥结果的概率分布是多少。
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_0", "criteria": null }, { "id": "o1", "name": "outcome_1", "criteria": null }, { "id": "o2", "name": "outcome_2", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.39375, 0.5270833333333333, 0.07916666666666666 ] }
一家翻译合作社的容器中装有 9 个标记令牌和 4 个未标记令牌。从中均匀且不放回地抽取恰好 3 个令牌,使得任意由 3 个独立令牌组成的子集被抽中的概率均相等。 一个探测器对抽出的样本进行检查并返回了一个阳性信号。在给定标记数量的条件下,其返回阳性信号的概率如下: 数量为 0 时:4/5; 数量为 1 时:19/20; 数量为 2 时:3/5; 数量为 3 时:3/20。
After the positive detector signal, what is the conditional distribution of the marked count?
[ { "id": "o0", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 1 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 0 marked tokens are drawn", "criteria": null }, { "id": "o3", "name": "...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.5628664495114006, 0.33420195439739414, 0.020846905537459284, 0.08208469055374593 ] }
A shipping depot has a container with 8 marked tokens and 17 unmarked tokens. Exactly 4 tokens are drawn uniformly WITHOUT replacement. Every subset of 4 individual tokens is equally likely.
What is the probability of each possible marked-token count?
[ { "id": "o0", "name": "Exactly 3 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 0 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 1 marked tokens are drawn", "criteria": null }, { "id": "o3", "name": "...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.07525691699604743, 0.18814229249011857, 0.4300395256916996, 0.30102766798418973, 0.005533596837944664 ] }
在一个条件事件模型中,定义了三个互斥的结果标签:outcome_0、outcome_1 和 outcome_2。该模型包含 15 个可能世界(worlds),每个世界具有特定的质量(mass)、观测状态(observed)和结果(outcome)。具体数据记录如下: 1. 质量为 6 的世界:已被观测到 (observed=true),结果为 outcome_2。 2. 质量为 2 的世界:已被观测到 (observed=true),结果为 outcome_0。 3. 质量为 17 的世界:已被观测到 (observed=true),结果为 outcome_0。 4. 质量为 15 的世界:未被观测到 (observed=fals...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_2", "criteria": null }, { "id": "o1", "name": "outcome_1", "criteria": null }, { "id": "o2", "name": "outcome_0", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.06666666666666667, 0.07777777777777778, 0.8555555555555555 ] }
这是一个随机工作流模型,包含八个互斥的最终结果,分别标记为:outcome_0、outcome_1、outcome_2、outcome_3、outcome_4、outcome_5、outcome_6 和 outcome_7。 初始状态概率分布如下: - outcome_0: 19/90 - outcome_1: 1/90 - outcome_2: 8/45 - outcome_3: 1/5 - outcome_4: 19/90 - outcome_5: 1/10 - outcome_6: 7/90 - outcome_7: 1/90 系统观测到的事件序列为 [2, 0]。 状态转移概率矩阵(行表示当前状态 outcome_0 ...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_6", "criteria": null }, { "id": "o1", "name": "outcome_4", "criteria": null }, { "id": "o2", "name": "outcome_0", "criteria": null }, { "id": "o3", "name": "outcome_1", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.006515776772955872, 0.04924835125278276, 0.018767774837555685, 0.05707325325496798, 0.041231743515076094, 0.7105710862716061, 0.012394636398513277, 0.10419737769654215 ] }
A botanical garden sensor has one of the listed hidden operating modes. Its report was censored: only the fact that the reading lies inside the alarm band is available. Use the alarm-band event, not a particular numeric reading. Mode violet: prior probability 2/13; probability of a reading inside the alarm band 3/5. Mo...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Operating mode ivory", "criteria": null }, { "id": "o1", "name": "Operating mode violet", "criteria": null }, { "id": "o2", "name": "Operating mode cobalt", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.6, 0.26666666666666666, 0.13333333333333333 ] }
A astronomy club has a container with 17 marked tokens and 17 unmarked tokens. Exactly 2 tokens are drawn uniformly WITHOUT replacement. Every subset of 2 individual tokens is equally likely. A detector examines the drawn sample and returned a positive signal. Conditional on the marked count, it has the following posit...
After the positive detector signal, what is the conditional distribution of the marked count?
[ { "id": "o0", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 1 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 0 marked tokens are drawn", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.21739130434782608, 0.7391304347826086, 0.043478260869565216 ] }
At a volunteer kitchen, exactly one of the following bins contains a missing item. Two inspectors each produce a positive or negative report. Their reports are conditionally independent given the true bin, not unconditionally independent. Both reports were positive. Bin hazel: prior 11/17; positive-report probability f...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Item is in bin indigo", "criteria": null }, { "id": "o1", "name": "Item is in bin hazel", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.5368421052631579, 0.4631578947368421 ] }
A decision model considers four mutually exclusive outcomes: outcome_0, outcome_1, outcome_2, and outcome_3. Before any new observations, the prior probabilities are assigned as follows: outcome_0 has a probability of 15/37, outcome_1 has 13/74, outcome_2 has 11/74, and outcome_3 has 10/37. Noisy evidence is observed,...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_0", "criteria": null }, { "id": "o1", "name": "outcome_2", "criteria": null }, { "id": "o2", "name": "outcome_1", "criteria": null }, { "id": "o3", "name": "outcome_3", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.09720176730486009, 0.1436426116838488, 0.41354933726067744, 0.34560628375061364 ] }
在一个条件事件模型中,我们关注三个互斥的结果:outcome_0、outcome_1 和 outcome_2。该模型由一系列具有特定质量(mass)的世界(worlds)构成,每个世界都标记了其是否被观测到(observed)以及实际发生的结果(outcome)。具体数据记录如下: - 一个质量为 16 的世界被观测到,其结果为 outcome_1。 - 一个质量为 19 的世界未被观测到,其结果为 outcome_1。 - 一个质量为 1 的世界被观测到,其结果为 outcome_0。 - 一个质量为 5 的世界被观测到,其结果为 outcome_1。 - 一个质量为 7 的世界未被观测到,其结果为 outcome_1。 - 一...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_1", "criteria": null }, { "id": "o1", "name": "outcome_0", "criteria": null }, { "id": "o2", "name": "outcome_2", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.8130081300813008, 0.18699186991869918, 0 ] }
At a public library, exactly one of the following bins contains a missing item. Two inspectors each produce a positive or negative report. Their reports are conditionally independent given the true bin, not unconditionally independent. Both reports were positive. Bin coral: prior 3/13; positive-report probability for i...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Item is in bin amber", "criteria": null }, { "id": "o1", "name": "Item is in bin cobalt", "criteria": null }, { "id": "o2", "name": "Item is in bin coral", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.3046875, 0.09375, 0.6015625 ] }
A translation cooperative receives items from three mutually exclusive suppliers: Supplier ruby, Supplier indigo, and Supplier cedar. The process for each item involves first passing a selection filter, followed by an inspection. For any given supplier, the event of an item being selected and the event of it receiving ...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Supplier ruby", "criteria": null }, { "id": "o1", "name": "Supplier indigo", "criteria": null }, { "id": "o2", "name": "Supplier cedar", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.2937365010799136, 0.08423326133909287, 0.6220302375809935 ] }
A wildlife rescue centre receives items from three mutually exclusive suppliers: Supplier cobalt, Supplier amber, and Supplier coral. Every item first passes through a selection filter and is subsequently inspected. For any given supplier, the event of an item being selected and the event of it receiving a positive ins...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Supplier coral", "criteria": null }, { "id": "o1", "name": "Supplier cobalt", "criteria": null }, { "id": "o2", "name": "Supplier amber", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.08532423208191127, 0.6143344709897611, 0.3003412969283277 ] }
一名志愿厨房调度员会在所有既符合资格又可用的服务中,选择成本最低的一项。如果没有任何服务同时符合资格且可用,则不选择任何服务。各服务的可用性事件相互独立,其概率如下所述;而服务的资格状态是已知且固定的。 - 服务 silver:成本 13;符合资格:是;可用概率:1/10。 - 服务 cedar:成本 6;符合资格:是;可用概率:7/20。 - 服务 amber:成本 10;符合资格:否;可用概率:1/20。 - 服务 ivory:成本 36;符合资格:否;可用概率:11/20。
What is the probability distribution of the service-selection outcome?
[ { "id": "o0", "name": "Select service ivory", "criteria": null }, { "id": "o1", "name": "No service is selected", "criteria": null }, { "id": "o2", "name": "Select service silver", "criteria": null }, { "id": "o3", "name": "Select service amber", "criteria...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0, 0.585, 0.065, 0, 0.35 ] }
A botanical garden dispatcher chooses the lowest-cost service among those that are both eligible and available. If none is eligible and available, no service is selected. Availability events are mutually independent, with the probabilities below; eligibility is already known and fixed. Service ruby: cost 20; eligible n...
What is the probability distribution of the service-selection outcome?
[ { "id": "o0", "name": "Select service amber", "criteria": null }, { "id": "o1", "name": "Select service ruby", "criteria": null }, { "id": "o2", "name": "Select service cedar", "criteria": null }, { "id": "o3", "name": "Select service ivory", "criteria": n...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.25, 0, 0.1575, 0.4875, 0.105 ] }
A translation cooperative process operates with two hidden states: indigo and amber. At each step, the process first transitions to a new state according to the transition table, and then emits an observed symbol based on that new state. This sequence repeats for every observed symbol. Given the hidden state sequence, ...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Final hidden state amber", "criteria": null }, { "id": "o1", "name": "Final hidden state indigo", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.7044245804936913, 0.2955754195063088 ] }
A shipping depot dispatcher chooses the lowest-cost service among those that are both eligible and available. If none is eligible and available, no service is selected. Availability events are mutually independent, with the probabilities below; eligibility is already known and fixed. Service cobalt: cost 17; eligible y...
What is the probability distribution of the service-selection outcome?
[ { "id": "o0", "name": "Select service cobalt", "criteria": null }, { "id": "o1", "name": "Select service ruby", "criteria": null }, { "id": "o2", "name": "Select service ivory", "criteria": null }, { "id": "o3", "name": "No service is selected", "criteria"...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.0456, 0.14, 0.8, 0.0114, 0.003, 0 ] }
A record of conditional events tracks four mutually exclusive outcomes: outcome_0, outcome_1, outcome_2, and outcome_3. The dataset consists of twenty distinct entries, each defined by a specific mass value, an observation status (either observed as true or false), and the associated outcome. The complete ledger is as ...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_2", "criteria": null }, { "id": "o1", "name": "outcome_3", "criteria": null }, { "id": "o2", "name": "outcome_1", "criteria": null }, { "id": "o3", "name": "outcome_0", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.2023121387283237, 0.09826589595375723, 0.2543352601156069, 0.44508670520231214 ] }
A robotics workshop sensor has one of the listed hidden operating modes. Its report was censored: only the fact that the reading lies inside the alarm band is available. Use the alarm-band event, not a particular numeric reading. Mode hazel: prior probability 13/24; probability of a reading inside the alarm band 19/20....
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Operating mode violet", "criteria": null }, { "id": "o1", "name": "Operating mode hazel", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.15120274914089346, 0.8487972508591065 ] }
A volunteer kitchen sensor has one of the listed hidden operating modes. Its report was censored: only the fact that the reading lies inside the alarm band is available. Use the alarm-band event, not a particular numeric reading. Mode cobalt: prior probability 3/14; probability of a reading inside the alarm band 1/4. M...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Operating mode violet", "criteria": null }, { "id": "o1", "name": "Operating mode ochre", "criteria": null }, { "id": "o2", "name": "Operating mode coral", "criteria": null }, { "id": "o3", "name": "Operating mode cobalt", "criteria"...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.20396600566572237, 0.509915014164306, 0.15864022662889518, 0.1274787535410765 ] }
A translation cooperative investigation uses the following exhaustive table of mutually exclusive scenarios. A scenario is drawn with probability proportional to its integer weight. The witnesses can share information; no independence assumption is allowed. We observed exactly the event named MATCH. Keep only scenarios...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Responsible person: Nolan", "criteria": null }, { "id": "o1", "name": "Responsible person: Quinn", "criteria": null }, { "id": "o2", "name": "Responsible person: Amira", "criteria": null }, { "id": "o3", "name": "Responsible person: Luis...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.5892857142857143, 0.4107142857142857, 0, 0 ] }
A community theatre has a container with 5 marked tokens and 13 unmarked tokens. Exactly 3 tokens are drawn uniformly WITHOUT replacement. Every subset of 3 individual tokens is equally likely. A detector examines the drawn sample and returned a positive signal. Conditional on the marked count, it has the following pos...
After the positive detector signal, what is the conditional distribution of the marked count?
[ { "id": "o0", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 3 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 1 marked tokens are drawn", "criteria": null }, { "id": "o3", "name": "...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.03680634201585504, 0.009909399773499434, 0.3864665911664779, 0.5668176670441676 ] }
A wildlife rescue centre has a container with 16 marked tokens and 10 unmarked tokens. Exactly 3 tokens are drawn uniformly WITHOUT replacement. Every subset of 3 individual tokens is equally likely.
What is the probability of each possible marked-token count?
[ { "id": "o0", "name": "Exactly 0 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 1 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o3", "name": "...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.046153846153846156, 0.27692307692307694, 0.46153846153846156, 0.2153846153846154 ] }
A stochastic workflow tracks the progression of a system through three mutually exclusive states, labeled outcome_0, outcome_1, and outcome_2. The process begins with an initial probability distribution where the system starts in outcome_0 with probability 1/7, in outcome_1 with probability 1/21, and in outcome_2 with ...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_2", "criteria": null }, { "id": "o1", "name": "outcome_0", "criteria": null }, { "id": "o2", "name": "outcome_1", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.033399981848461234, 0.06694282451688706, 0.8996571936346517 ] }
在一个包含六个互斥潜在状态(标记为 outcome_0, outcome_1, outcome_2, outcome_3, outcome_4, outcome_5)的决策模型中,系统遵循以下概率设定: 初始状态概率分布如下:outcome_0 为 8/55,outcome_1 为 1/11,outcome_2 为 3/11,outcome_3 为 1/5,outcome_4 为 7/55,outcome_5 为 9/55。 状态转移概率矩阵(行代表当前状态 outcome_0 至 outcome_5,列代表下一时刻状态 outcome_0 至 outcome_5)定义为: - 若当前为 outcome_0:转移至 outcom...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_1", "criteria": null }, { "id": "o1", "name": "outcome_3", "criteria": null }, { "id": "o2", "name": "outcome_4", "criteria": null }, { "id": "o3", "name": "outcome_2", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.004517057274363126, 0.02605545340822302, 0.03278569014821568, 0.041680203036189904, 0.8405872072896495, 0.05437438884335875 ] }
A system evolves through six mutually exclusive latent states labeled outcome_0, outcome_1, outcome_2, outcome_3, outcome_4, and outcome_5. The process begins with the following initial probability distribution: outcome_0 has a probability of 6/35, outcome_1 is 9/35, outcome_2 is 1/5, outcome_3 is 4/35, outcome_4 is 2/...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_4", "criteria": null }, { "id": "o1", "name": "outcome_2", "criteria": null }, { "id": "o2", "name": "outcome_3", "criteria": null }, { "id": "o3", "name": "outcome_0", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.3044763083586161, 0.15089749018478726, 0.06103402122066891, 0.156917314719371, 0.1154834366027238, 0.21119142891383294 ] }
At a translation cooperative, exactly one of the following bins contains a missing item. Two inspectors each produce a positive or negative report. Their reports are conditionally independent given the true bin, not unconditionally independent. Both reports were positive. Bin cedar: prior 11/25; positive-report probabi...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Item is in bin ruby", "criteria": null }, { "id": "o1", "name": "Item is in bin amber", "criteria": null }, { "id": "o2", "name": "Item is in bin cedar", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.8491228070175438, 0.07368421052631578, 0.07719298245614035 ] }
A translation cooperative has a container with 7 marked tokens and 11 unmarked tokens. Exactly 4 tokens are drawn uniformly WITHOUT replacement. Every subset of 4 individual tokens is equally likely. A detector examines the drawn sample and returned a positive signal. Conditional on the marked count, it has the followi...
After the positive detector signal, what is the conditional distribution of the marked count?
[ { "id": "o0", "name": "Exactly 0 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 3 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 1 marked tokens are drawn", "criteria": null }, { "id": "o3", "name": "...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.12354409317803661, 0.04804492512479201, 0.3603369384359401, 0.011647254575707155, 0.4564267886855241 ] }
在一个有限的贝叶斯决策模型中,我们考虑十二个互斥的结果,分别标记为 outcome_0 至 outcome_11。在观察到特定证据之前,这些结果的先验概率分布如下:outcome_0 为 23/165,outcome_1 为 16/165,outcome_2 为 7/330,outcome_3 为 3/22,outcome_4 为 14/165,outcome_5 为 4/55,outcome_6 为 8/55,outcome_7 为 4/55,outcome_8 为 1/30,outcome_9 为 7/66,outcome_10 为 1/22,outcome_11 为 1/22。在给定该证据发生的条件下,各结果产生该证据的似然度...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_2", "criteria": null }, { "id": "o1", "name": "outcome_9", "criteria": null }, { "id": "o2", "name": "outcome_10", "criteria": null }, { "id": "o3", "name": "outcome_6", "criteria": null }, { "id": "o4", "name": "...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.03484898771988052, 0.08131430467972121, 0.0448058413541321, 0.06372386325921009, 0.05310321938267507, 0.009293063391968137, 0.2688350481247926, 0.12744772651842018, 0.12744772651842018, 0.12213740458015267, 0.062064387653501495, ...
在一个有限的贝叶斯决策模型中,我们考虑六个互斥的结果,分别标记为 outcome_0、outcome_1、outcome_2、outcome_3、outcome_4 和 outcome_5。在观测到特定证据之前,这些结果的先验概率分布如下:outcome_0 为 1/34,outcome_1 为 1/34,outcome_2 为 23/102,outcome_3 为 19/51,outcome_4 为 4/51,outcome_5 为 9/34。在给定该证据的条件下,各结果产生该观测值的似然度(条件概率)分别为:outcome_0 是 9/10,outcome_1 是 1/4,outcome_2 是 3/20,outcome_3 是...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_3", "criteria": null }, { "id": "o1", "name": "outcome_2", "criteria": null }, { "id": "o2", "name": "outcome_0", "criteria": null }, { "id": "o3", "name": "outcome_4", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.5048715677590788, 0.06111603188662533, 0.047829937998228524, 0.0141718334809566, 0.013286093888396812, 0.3587245349867139 ] }
A decision model evaluates six mutually exclusive outcomes: outcome_0, outcome_1, outcome_2, outcome_3, outcome_4, and outcome_5. Before any new evidence is considered, the prior probabilities for these outcomes are established as follows: outcome_0 is 10/61, outcome_1 is 29/122, outcome_2 is 35/122, outcome_3 is 16/61...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_3", "criteria": null }, { "id": "o1", "name": "outcome_5", "criteria": null }, { "id": "o2", "name": "outcome_4", "criteria": null }, { "id": "o3", "name": "outcome_2", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.1674808094905792, 0.011339846475924634, 0.01256106071179344, 0.6594556873691556, 0.12648290300069784, 0.022679692951849267 ] }
A wildlife rescue centre sensor has one of the listed hidden operating modes. Its report was censored: only the fact that the reading lies inside the alarm band is available. Use the alarm-band event, not a particular numeric reading. Mode ochre: prior probability 7/26; probability of a reading inside the alarm band 1/...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Operating mode ochre", "criteria": null }, { "id": "o1", "name": "Operating mode hazel", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.15555555555555556, 0.8444444444444444 ] }
A community theatre maintains a container holding 5 marked tokens and 6 unmarked tokens. Two tokens are drawn from this container uniformly at random without replacement, ensuring that every possible subset of two individual tokens has an equal chance of being selected.
What is the probability of each possible marked-token count?
[ { "id": "o0", "name": "Exactly 1 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 0 marked tokens are drawn", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.5454545454545454, 0.18181818181818182, 0.2727272727272727 ] }
A volunteer kitchen maintains a container holding 5 marked tokens and 13 unmarked tokens. From this container, exactly 4 tokens are drawn uniformly at random without replacement, ensuring that every possible subset of 4 individual tokens has an equal chance of being selected. A detector then examines the drawn sample a...
After the positive detector signal, what is the conditional distribution of the marked count?
[ { "id": "o0", "name": "Exactly 4 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 3 marked tokens are drawn", "criteria": null }, { "id": "o3", "name": "...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.0005737234652897303, 0.28640275387263336, 0.023866896156052784, 0.06563396442914515, 0.6235226620768789 ] }
A museum archive process has hidden states violet, hazel, jade. At each step, it FIRST changes state using the transition table and THEN emits the observed symbol using the new state. This repeats for every observed symbol. Conditional on the hidden state sequence, emissions are independent. State order in every vector...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Final hidden state violet", "criteria": null }, { "id": "o1", "name": "Final hidden state jade", "criteria": null }, { "id": "o2", "name": "Final hidden state hazel", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.504069240099746, 0.12082094807681507, 0.37510981182343894 ] }
A astronomy club dispatcher chooses the lowest-cost service among those that are both eligible and available. If none is eligible and available, no service is selected. Availability events are mutually independent, with the probabilities below; eligibility is already known and fixed. Service jade: cost 33; eligible yes...
What is the probability distribution of the service-selection outcome?
[ { "id": "o0", "name": "Select service jade", "criteria": null }, { "id": "o1", "name": "No service is selected", "criteria": null }, { "id": "o2", "name": "Select service hazel", "criteria": null }, { "id": "o3", "name": "Select service amber", "criteria":...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.0425, 0.3674125, 0.24225, 0.15, 0.1978375 ] }
A wildlife rescue centre sensor operates in one of three hidden modes: silver, jade, or ruby. The sensor's specific numeric reading has been censored; the only available information is that the reading falls within the alarm band. The prior probabilities for the modes are as follows: mode silver is 16/25, mode jade is ...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Operating mode jade", "criteria": null }, { "id": "o1", "name": "Operating mode silver", "criteria": null }, { "id": "o2", "name": "Operating mode ruby", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.04395604395604396, 0.8791208791208791, 0.07692307692307693 ] }
A robotics workshop has a container with 6 marked tokens and 11 unmarked tokens. Exactly 2 tokens are drawn uniformly WITHOUT replacement. Every subset of 2 individual tokens is equally likely.
What is the probability of each possible marked-token count?
[ { "id": "o0", "name": "Exactly 0 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 1 marked tokens are drawn", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.40441176470588236, 0.11029411764705882, 0.4852941176470588 ] }
A dispatcher at a botanical garden follows a strict protocol: they must select the lowest-cost service among those that are both eligible and currently available. If no service meets both criteria, no selection is made. Eligibility is fixed and confirmed for all three options: Service Hazel (cost 31), Service Ivory (co...
What is the probability distribution of the service-selection outcome?
[ { "id": "o0", "name": "Select service silver", "criteria": null }, { "id": "o1", "name": "Select service ivory", "criteria": null }, { "id": "o2", "name": "Select service hazel", "criteria": null }, { "id": "o3", "name": "No service is selected", "criteria...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.014, 0.2, 0.76, 0.026 ] }
A astronomy club has a container with 13 marked tokens and 17 unmarked tokens. Exactly 4 tokens are drawn uniformly WITHOUT replacement. Every subset of 4 individual tokens is equally likely.
What is the probability of each possible marked-token count?
[ { "id": "o0", "name": "Exactly 0 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 3 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 1 marked tokens are drawn", "criteria": null }, { "id": "o3", "name": "...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.08684546615581099, 0.17741288086115672, 0.32256887429301223, 0.38708264915161467, 0.0260901295384054 ] }
A system evolves through six mutually exclusive latent states, labeled outcome_0, outcome_1, outcome_2, outcome_3, outcome_4, and outcome_5. The process begins with the following initial probability distribution across these states: - outcome_0: 13/58 - outcome_1: 7/58 - outcome_2: 19/58 - outcome_3: 11/58 - outcome_...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_1", "criteria": null }, { "id": "o1", "name": "outcome_5", "criteria": null }, { "id": "o2", "name": "outcome_4", "criteria": null }, { "id": "o3", "name": "outcome_2", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.09030334397053422, 0.11775743377947646, 0.3390323778578276, 0.13161260892658988, 0.06665843460873172, 0.2546358008568402 ] }
A measurement system operates with uncertainty regarding true readings in millimetres, where the possible true values are 17, 50, 95, 112, and 154. Before any observation, the prior probabilities for these respective readings are 26/69, 22/69, 11/69, 3/23, and 1/69. Upon receiving an observed signal labeled 'sensor_pos...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "154", "criteria": null }, { "id": "o1", "name": "112", "criteria": null }, { "id": "o2", "name": "95", "criteria": null }, { "id": "o3", "name": "17", "criteria": null }, { "id": "o4", "name": "50", "criteria": null ...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.01913265306122449, 0.10331632653061225, 0.25255102040816324, 0.5969387755102041, 0.02806122448979592 ] }
A record of twenty distinct events has been compiled, each assigned a specific mass value and classified by an observed status (true or false) and an outcome label (outcome_0, outcome_1, outcome_2, or outcome_3). The data points are as follows: 1. An event with mass 7 was observed and resulted in outcome_2. 2. An even...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_0", "criteria": null }, { "id": "o1", "name": "outcome_2", "criteria": null }, { "id": "o2", "name": "outcome_3", "criteria": null }, { "id": "o3", "name": "outcome_1", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.4583333333333333, 0.15625, 0.296875, 0.08854166666666667 ] }
A finite Bayesian model is defined with three mutually exclusive outcomes labeled outcome_0, outcome_1, and outcome_2. The prior probabilities assigned to these outcomes are 19/43 for outcome_0, 8/43 for outcome_1, and 16/43 for outcome_2. The likelihoods associated with the stated observations are 7/10 for outcome_0, ...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_0", "criteria": null }, { "id": "o1", "name": "outcome_2", "criteria": null }, { "id": "o2", "name": "outcome_1", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.6018099547511312, 0.36199095022624433, 0.03619909502262444 ] }
A museum archive has a container with 5 marked tokens and 14 unmarked tokens. Exactly 4 tokens are drawn uniformly WITHOUT replacement. Every subset of 4 individual tokens is equally likely. A detector examines the drawn sample and returned a positive signal. Conditional on the marked count, it has the following positi...
After the positive detector signal, what is the conditional distribution of the marked count?
[ { "id": "o0", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 3 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 4 marked tokens are drawn", "criteria": null }, { "id": "o3", "name": "...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.13024986709197237, 0.01145053776632724, 0.0005111847217110375, 0.63264221158958, 0.22514619883040934 ] }
At a museum archive, exactly one of the following bins contains a missing item. Two inspectors each produce a positive or negative report. Their reports are conditionally independent given the true bin, not unconditionally independent. Both reports were positive. Bin cedar: prior 7/23; positive-report probability for i...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Item is in bin indigo", "criteria": null }, { "id": "o1", "name": "Item is in bin cedar", "criteria": null }, { "id": "o2", "name": "Item is in bin coral", "criteria": null }, { "id": "o3", "name": "Item is in bin cobalt", "criteria"...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.4924889543446245, 0.4639175257731959, 0.04241531664212077, 0.00117820324005891 ] }
A sampling process is conducted without replacement. The population consists of 33 items labeled as successes and 125 items labeled as failures, with labels drawn from the set ["0", "1", "2", "3"]. A total of 3 draws are made from this population.
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "2", "criteria": null }, { "id": "o1", "name": "0", "criteria": null }, { "id": "o2", "name": "3", "criteria": null }, { "id": "o3", "name": "1", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.10233256222129881, 0.49266926736087424, 0.008459491810294036, 0.3965386786075329 ] }
A community theatre maintains a container holding 16 marked tokens and 6 unmarked tokens. Two tokens are drawn uniformly at random without replacement, ensuring every possible pair of tokens is equally likely to be selected. A detector examines the drawn sample and returns a positive signal. The probability of this pos...
After the positive detector signal, what is the conditional distribution of the marked count?
[ { "id": "o0", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 1 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 0 marked tokens are drawn", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.38004750593824227, 0.6080760095011877, 0.011876484560570071 ] }
A sports club investigation uses the following exhaustive table of mutually exclusive scenarios. A scenario is drawn with probability proportional to its integer weight. The witnesses can share information; no independence assumption is allowed. We observed exactly the event named MATCH. Keep only scenarios whose obser...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Responsible person: Sofia", "criteria": null }, { "id": "o1", "name": "Responsible person: Hugo", "criteria": null }, { "id": "o2", "name": "Responsible person: Quinn", "criteria": null }, { "id": "o3", "name": "Responsible person: Benoi...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.391304347826087, 0, 0.6086956521739131, 0 ] }
A system evolves through three latent states labeled outcome_0, outcome_1, and outcome_2. The process begins with an initial probability distribution across these states: outcome_0 has a probability of 1/22, outcome_1 has a probability of 8/11, and outcome_2 has a probability of 5/22. The system transitions between th...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_0", "criteria": null }, { "id": "o1", "name": "outcome_1", "criteria": null }, { "id": "o2", "name": "outcome_2", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.23384399566122516, 0.4987271726184698, 0.26742883172030496 ] }
A botanical garden process operates with two hidden states: indigo and coral. At each step, the process first transitions to a new state using the specified transition probabilities, and then emits an observed symbol based on that new state. This sequence repeats for every observed symbol. Given the hidden state sequen...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Final hidden state coral", "criteria": null }, { "id": "o1", "name": "Final hidden state indigo", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.7238246919616802, 0.27617530803831986 ] }
A selection censoring model is defined over four mutually exclusive outcomes: outcome_0, outcome_1, outcome_2, and outcome_3. The prior probabilities for these outcomes are established as follows: outcome_0 has a prior of 9/107, outcome_1 has a prior of 85/107, outcome_2 has a prior of 7/107, and outcome_3 has a prior ...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_3", "criteria": null }, { "id": "o1", "name": "outcome_0", "criteria": null }, { "id": "o2", "name": "outcome_1", "criteria": null }, { "id": "o3", "name": "outcome_2", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.1067853170189099, 0.007150802478944859, 0.8104242809470841, 0.07563959955506118 ] }
A measurement uncertainty model is defined for possible true readings in millimetres, with candidate values of 15, 16, 20, 38, 60, 81, 92, 94, 148, 154, 170, and 180. The prior probabilities assigned to these respective readings are 33/251, 28/251, 5/251, 31/251, 41/251, 1/251, 17/251, 2/251, 19/251, 22/251, 5/251, and...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "154", "criteria": null }, { "id": "o1", "name": "170", "criteria": null }, { "id": "o2", "name": "16", "criteria": null }, { "id": "o3", "name": "60", "criteria": null }, { "id": "o4", "name": "92", "criteria": null ...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.12021857923497267, 0.025220680958385876, 0.1176965111391341, 0.15510718789407313, 0.057166876839007986, 0.20849096258932326, 0.014291719209751997, 0.18032786885245902, 0.07986548970155527, 0.014712063892391762, 0.019756200084068937, ...
A system evolves through six mutually exclusive latent states labeled outcome_0, outcome_1, outcome_2, outcome_3, outcome_4, and outcome_5. At the initial time step, the probability distribution across these states is as follows: outcome_0 has a probability of 1/3; outcome_1, 2/51; outcome_2, 4/51; outcome_3, 10/51; ou...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_2", "criteria": null }, { "id": "o1", "name": "outcome_5", "criteria": null }, { "id": "o2", "name": "outcome_4", "criteria": null }, { "id": "o3", "name": "outcome_0", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.02367436863005703, 0.00740870940683005, 0.02637996403837548, 0.8559974372234572, 0.05199031603021073, 0.03454920467106943 ] }
A selection censoring model is defined over five mutually exclusive outcomes: outcome_0, outcome_1, outcome_2, outcome_3, and outcome_4. The prior probabilities for these outcomes are assigned as follows: outcome_0 has a prior of 1/3; outcome_1 has a prior of 3/46; outcome_2 has a prior of 25/138; outcome_3 has a prior...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_3", "criteria": null }, { "id": "o1", "name": "outcome_1", "criteria": null }, { "id": "o2", "name": "outcome_2", "criteria": null }, { "id": "o3", "name": "outcome_0", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.27401755055322397, 0.026440289965661962, 0.022892025944296072, 0.5335368180083937, 0.14311331552842427 ] }
A astronomy club has a container with 14 marked tokens and 8 unmarked tokens. Exactly 2 tokens are drawn uniformly WITHOUT replacement. Every subset of 2 individual tokens is equally likely. A detector examines the drawn sample and returned a positive signal. Conditional on the marked count, it has the following positi...
After the positive detector signal, what is the conditional distribution of the marked count?
[ { "id": "o0", "name": "Exactly 1 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 0 marked tokens are drawn", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.1813031161473088, 0.6260623229461756, 0.19263456090651557 ] }
A translation cooperative investigation uses the following exhaustive table of mutually exclusive scenarios. A scenario is drawn with probability proportional to its integer weight. The witnesses can share information; no independence assumption is allowed. We observed exactly the event named MATCH. Keep only scenarios...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Responsible person: Farid", "criteria": null }, { "id": "o1", "name": "Responsible person: Uma", "criteria": null }, { "id": "o2", "name": "Responsible person: Benoit", "criteria": null }, { "id": "o3", "name": "Responsible person: Amira...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.37254901960784315, 0, 0.1568627450980392, 0.47058823529411764 ] }
A system evolves through six mutually exclusive latent states, labeled outcome_0, outcome_1, outcome_2, outcome_3, outcome_4, and outcome_5. The process begins with the following initial probability distribution across these states: - outcome_0: 18/49 - outcome_1: 2/49 - outcome_2: 1/7 - outcome_3: 9/49 - outcome_4: ...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_1", "criteria": null }, { "id": "o1", "name": "outcome_5", "criteria": null }, { "id": "o2", "name": "outcome_0", "criteria": null }, { "id": "o3", "name": "outcome_2", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.06571762975867246, 0.02000373990735999, 0.04560683102844645, 0.04530536582860467, 0.797867101884204, 0.025499331592712466 ] }
At a botanical garden, a missing item is located in exactly one of three bins: ruby, amber, or cedar. The prior probability that the item is in bin ruby is 7/19, in bin amber is 9/38, and in bin cedar is 15/38. Two inspectors each issued a report, and both reports were positive. The probability of a positive report dep...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Item is in bin cedar", "criteria": null }, { "id": "o1", "name": "Item is in bin amber", "criteria": null }, { "id": "o2", "name": "Item is in bin ruby", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.4003954522985665, 0.2535837864557588, 0.3460207612456747 ] }
A system evolves through eight mutually exclusive latent states, labeled outcome_0 through outcome_7. The process begins with the following initial probability distribution across these states: outcome_0 is 2/35, outcome_1 is 6/35, outcome_2 is 8/105, outcome_3 is 4/35, outcome_4 is 11/105, outcome_5 is 6/35, outcome_6...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_6", "criteria": null }, { "id": "o1", "name": "outcome_3", "criteria": null }, { "id": "o2", "name": "outcome_4", "criteria": null }, { "id": "o3", "name": "outcome_1", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.024975822727039368, 0.1256282081379124, 0.07903337327431287, 0.061742450721793345, 0.569310789560666, 0.0184397909754343, 0.03519824545396261, 0.08567131914887907 ] }
A system evolves through eight mutually exclusive latent states, labeled outcome_0 through outcome_7. The process begins with an initial probability distribution across these states as follows: outcome_0 is 11/68, outcome_1 is 1/17, outcome_2 is 1/4, outcome_3 is 2/17, outcome_4 is 1/34, outcome_5 is 4/17, outcome_6 is...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_4", "criteria": null }, { "id": "o1", "name": "outcome_2", "criteria": null }, { "id": "o2", "name": "outcome_5", "criteria": null }, { "id": "o3", "name": "outcome_0", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.10186191207664821, 0.18567161301655483, 0.10914906088522519, 0.20208408720618, 0.08787414439350377, 0.05206843891116751, 0.09708451217025058, 0.16420623134046988 ] }
A museum archive receives items from mutually exclusive suppliers. An item first passes a selection filter, then is inspected. Given its supplier, selection and a positive inspection are independent. The observed item was selected AND inspected positive; both pieces of evidence must be conditioned on. Supplier cedar: f...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Supplier cedar", "criteria": null }, { "id": "o1", "name": "Supplier jade", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.19822320932815102, 0.8017767906718489 ] }
野外研究站的一个容器中装有 14 个标记代币和 13 个未标记代币。从中均匀且不放回地恰好抽取 2 个代币,任意由 2 个独立代币组成的子集被抽中的概率均相等。 一个探测器对抽取的样本进行检查并返回了阳性信号。在给定标记数量的条件下,其返回阳性信号的概率如下: 数量为 0 时:19/20; 数量为 1 时:13/20; 数量为 2 时:2/5。
After the positive detector signal, what is the conditional distribution of the marked count?
[ { "id": "o0", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 1 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 0 marked tokens are drawn", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.1590909090909091, 0.5170454545454546, 0.32386363636363635 ] }
A wildlife rescue centre sensor operates in one of three hidden modes: cedar, ochre, or cobalt. The specific numeric reading from the sensor has been censored; the only available information is that the reading falls within the alarm band. The prior probabilities and the conditional probabilities of a reading falling i...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Operating mode cedar", "criteria": null }, { "id": "o1", "name": "Operating mode ochre", "criteria": null }, { "id": "o2", "name": "Operating mode cobalt", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.029411764705882353, 0.17647058823529413, 0.7941176470588235 ] }
A finite Bayesian model is defined over twelve mutually exclusive outcomes, labeled outcome_0 through outcome_11. Before any specific observations are made, the prior probabilities for these outcomes are established as follows: outcome_0 is 26/293, outcome_1 is 25/293, outcome_2 is 11/293, outcome_3 is 41/293, outcome_...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_0", "criteria": null }, { "id": "o1", "name": "outcome_10", "criteria": null }, { "id": "o2", "name": "outcome_8", "criteria": null }, { "id": "o3", "name": "outcome_11", "criteria": null }, { "id": "o4", "name": ...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.09591373439273553, 0.04086265607264472, 0.12258796821793416, 0.19409761634506242, 0.14982973893303064, 0.009648127128263337, 0.0019863791146424517, 0.09931895573212259, 0.09931895573212259, 0.08144154370034053, 0.04370034052213394, ...
A record of conditional events lists twenty distinct worlds, each characterized by an outcome label (outcome_0, outcome_1, outcome_2, or outcome_3), a mass value, and an observation status (observed: true or observed: false). The specific entries are as follows: 1. Outcome: outcome_1, Mass: 9, Observed: Yes 2. Outcome...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_1", "criteria": null }, { "id": "o1", "name": "outcome_0", "criteria": null }, { "id": "o2", "name": "outcome_3", "criteria": null }, { "id": "o3", "name": "outcome_2", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.35135135135135137, 0.3063063063063063, 0.2702702702702703, 0.07207207207207207 ] }
一个野外研究站有一个容器,里面装有 13 个标记代币和 11 个未标记代币。从中不放回地均匀抽取恰好 4 个代币。任意由 4 个独立代币组成的子集被抽中的可能性均相等。
What is the probability of each possible marked-token count?
[ { "id": "o0", "name": "Exactly 3 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 4 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 0 marked tokens are drawn", "criteria": null }, { "id": "o3", "name": "...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.29606625258799174, 0.06728778467908902, 0.031055900621118012, 0.20186335403726707, 0.40372670807453415 ] }
A decision model evaluates four mutually exclusive outcomes: outcome_0, outcome_1, outcome_2, and outcome_3. Before any new evidence is considered, the prior probabilities are assigned as follows: outcome_0 has a probability of 8/93, outcome_1 has 4/31, outcome_2 has 32/93, and outcome_3 has 41/93. The model incorpora...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_1", "criteria": null }, { "id": "o1", "name": "outcome_3", "criteria": null }, { "id": "o2", "name": "outcome_0", "criteria": null }, { "id": "o3", "name": "outcome_2", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.10381050463439753, 0.6333676622039135, 0.032131822863027806, 0.23069001029866118 ] }
At a public library, exactly one of the following bins contains a missing item. Two inspectors each produce a positive or negative report. Their reports are conditionally independent given the true bin, not unconditionally independent. Both reports were positive. Bin coral: prior 7/43; positive-report probability for i...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Item is in bin jade", "criteria": null }, { "id": "o1", "name": "Item is in bin coral", "criteria": null }, { "id": "o2", "name": "Item is in bin amber", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.798499061913696, 0.08667917448405253, 0.11482176360225141 ] }
A community theatre receives items from four mutually exclusive suppliers: Supplier jade, Supplier cedar, Supplier coral, and Supplier ochre. Every item first passes through a selection filter and is subsequently inspected. For any given supplier, the event of an item being selected and the event of it receiving a posi...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Supplier jade", "criteria": null }, { "id": "o1", "name": "Supplier cedar", "criteria": null }, { "id": "o2", "name": "Supplier coral", "criteria": null }, { "id": "o3", "name": "Supplier ochre", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.0967741935483871, 0.4107965766951942, 0.04739960500329164, 0.4450296247531271 ] }
A field research station has a container with 5 marked tokens and 6 unmarked tokens. Exactly 3 tokens are drawn uniformly WITHOUT replacement. Every subset of 3 individual tokens is equally likely.
What is the probability of each possible marked-token count?
[ { "id": "o0", "name": "Exactly 0 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 1 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o3", "name": "...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.12121212121212122, 0.45454545454545453, 0.36363636363636365, 0.06060606060606061 ] }
A public library receives items from three mutually exclusive suppliers: Supplier ruby, Supplier violet, and Supplier cedar. The process for each item involves first passing a selection filter, followed by an inspection. For any given supplier, the event of an item being selected and the event of it receiving a positiv...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Supplier cedar", "criteria": null }, { "id": "o1", "name": "Supplier violet", "criteria": null }, { "id": "o2", "name": "Supplier ruby", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.7431635388739947, 0.0836461126005362, 0.17319034852546916 ] }
A translation cooperative receives items from mutually exclusive suppliers. An item first passes a selection filter, then is inspected. Given its supplier, selection and a positive inspection are independent. The observed item was selected AND inspected positive; both pieces of evidence must be conditioned on. Supplier...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Supplier jade", "criteria": null }, { "id": "o1", "name": "Supplier ivory", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.8523862375138734, 0.14761376248612654 ] }
A botanical garden investigation uses the following exhaustive table of mutually exclusive scenarios. A scenario is drawn with probability proportional to its integer weight. The witnesses can share information; no independence assumption is allowed. We observed exactly the event named MATCH. Keep only scenarios whose ...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Responsible person: Sofia", "criteria": null }, { "id": "o1", "name": "Responsible person: Priya", "criteria": null }, { "id": "o2", "name": "Responsible person: Ravi", "criteria": null }, { "id": "o3", "name": "Responsible person: Tariq...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.056179775280898875, 0.2696629213483146, 0.6741573033707865, 0 ] }
A community theatre sensor has one of the listed hidden operating modes. Its report was censored: only the fact that the reading lies inside the alarm band is available. Use the alarm-band event, not a particular numeric reading. Mode silver: prior probability 13/20; probability of a reading inside the alarm band 19/20...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Operating mode silver", "criteria": null }, { "id": "o1", "name": "Operating mode violet", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.9216417910447762, 0.07835820895522388 ] }
A selection censoring model is defined over five mutually exclusive outcomes: outcome_0, outcome_1, outcome_2, outcome_3, and outcome_4. The prior probabilities for these outcomes are assigned as follows: outcome_0 has a prior of 13/129, outcome_1 has a prior of 3/43, outcome_2 has a prior of 31/129, outcome_3 has a pr...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_2", "criteria": null }, { "id": "o1", "name": "outcome_4", "criteria": null }, { "id": "o2", "name": "outcome_3", "criteria": null }, { "id": "o3", "name": "outcome_1", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.5381165919282511, 0.3020396354694055, 0.09518298857225517, 0.019528424707073628, 0.04513235932301461 ] }
A volunteer kitchen dispatcher chooses the lowest-cost service among those that are both eligible and available. If none is eligible and available, no service is selected. Availability events are mutually independent, with the probabilities below; eligibility is already known and fixed. Service cedar: cost 39; eligible...
What is the probability distribution of the service-selection outcome?
[ { "id": "o0", "name": "Select service jade", "criteria": null }, { "id": "o1", "name": "Select service cedar", "criteria": null }, { "id": "o2", "name": "Select service ochre", "criteria": null }, { "id": "o3", "name": "No service is selected", "criteria":...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0, 0.105, 0.14, 0.105, 0.65 ] }
A system evolves through six mutually exclusive latent states, labeled outcome_0, outcome_1, outcome_2, outcome_3, outcome_4, and outcome_5. At the initial time step, the probability distribution across these states is as follows: outcome_0 has a probability of 14/61, outcome_1 is 16/61, outcome_2 is 9/61, outcome_3 is...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_1", "criteria": null }, { "id": "o1", "name": "outcome_3", "criteria": null }, { "id": "o2", "name": "outcome_0", "criteria": null }, { "id": "o3", "name": "outcome_4", "criteria": null }, { "id": "o4", "name": "o...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.051939430852262276, 0.058254821938333014, 0.07937387488035845, 0.12533888343754665, 0.5637096402892431, 0.12138334860225647 ] }
A museum archive has a container with 4 marked tokens and 14 unmarked tokens. Exactly 2 tokens are drawn uniformly WITHOUT replacement. Every subset of 2 individual tokens is equally likely.
What is the probability of each possible marked-token count?
[ { "id": "o0", "name": "Exactly 0 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 1 marked tokens are drawn", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.5947712418300654, 0.0392156862745098, 0.3660130718954248 ] }
A selection censoring model is defined with three mutually exclusive outcomes: outcome_0, outcome_1, and outcome_2. The prior probabilities for these outcomes are 6/173, 11/173, and 156/173, respectively. The model includes likelihood data structured as pairs for each outcome: for outcome_0, the likelihoods are 1/10 an...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_2", "criteria": null }, { "id": "o1", "name": "outcome_0", "criteria": null }, { "id": "o2", "name": "outcome_1", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.8740359897172236, 0.006327862368993475, 0.11963614791378288 ] }
A measurement system is assessing a true reading in millimetres, which is known to be one of three mutually exclusive values: 33, 97, or 137. Before any new data is considered, the prior probabilities for these true readings are assigned as follows: 2/5 for 33 mm, 4/15 for 97 mm, and 1/3 for 137 mm. The system has now ...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "33", "criteria": null }, { "id": "o1", "name": "97", "criteria": null }, { "id": "o2", "name": "137", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.5454545454545454, 0.2597402597402597, 0.19480519480519481 ] }
A museum archive sensor has one of the listed hidden operating modes. Its report was censored: only the fact that the reading lies inside the alarm band is available. Use the alarm-band event, not a particular numeric reading. Mode coral: prior probability 3/11; probability of a reading inside the alarm band 11/20. Mod...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Operating mode ivory", "criteria": null }, { "id": "o1", "name": "Operating mode coral", "criteria": null }, { "id": "o2", "name": "Operating mode silver", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.7077363896848138, 0.18911174785100288, 0.10315186246418338 ] }
A botanical garden dispatcher chooses the lowest-cost service among those that are both eligible and available. If none is eligible and available, no service is selected. Availability events are mutually independent, with the probabilities below; eligibility is already known and fixed. Service hazel: cost 25; eligible ...
What is the probability distribution of the service-selection outcome?
[ { "id": "o0", "name": "Select service jade", "criteria": null }, { "id": "o1", "name": "No service is selected", "criteria": null }, { "id": "o2", "name": "Select service cobalt", "criteria": null }, { "id": "o3", "name": "Select service hazel", "criteria"...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.0625, 0.0028125, 0.75, 0.09375, 0.001875, 0.0890625 ] }
A shipping depot has a container with 4 marked tokens and 11 unmarked tokens. Exactly 2 tokens are drawn uniformly WITHOUT replacement. Every subset of 2 individual tokens is equally likely. A detector examines the drawn sample and returned a positive signal. Conditional on the marked count, it has the following positi...
After the positive detector signal, what is the conditional distribution of the marked count?
[ { "id": "o0", "name": "Exactly 0 marked tokens are drawn", "criteria": null }, { "id": "o1", "name": "Exactly 2 marked tokens are drawn", "criteria": null }, { "id": "o2", "name": "Exactly 1 marked tokens are drawn", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.7403008709422011, 0.0855106888361045, 0.17418844022169439 ] }
A selection censoring model is defined with three mutually exclusive outcomes: outcome_0, outcome_1, and outcome_2. The prior probabilities for these outcomes are 15/29 for outcome_0, 3/29 for outcome_1, and 11/29 for outcome_2. The likelihoods are structured as pairs corresponding to specific observations: for outcome...
What is the probability distribution over the mutually exclusive listed outcomes, conditional on the stated observations?
[ { "id": "o0", "name": "outcome_0", "criteria": null }, { "id": "o1", "name": "outcome_1", "criteria": null }, { "id": "o2", "name": "outcome_2", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.7475083056478405, 0.17940199335548174, 0.07308970099667775 ] }
An astronomy club dispatcher follows a strict protocol to choose a service: they select the lowest-cost option among those that are both eligible and available. If no service meets both criteria, no service is selected. Eligibility status is fixed and known in advance, while availability events occur independently with...
What is the probability distribution of the service-selection outcome?
[ { "id": "o0", "name": "No service is selected", "criteria": null }, { "id": "o1", "name": "Select service ochre", "criteria": null }, { "id": "o2", "name": "Select service ivory", "criteria": null }, { "id": "o3", "name": "Select service coral", "criteria"...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.33, 0.45, 0.22, 0 ] }
A museum archive receives items from mutually exclusive suppliers. An item first passes a selection filter, then is inspected. Given its supplier, selection and a positive inspection are independent. The observed item was selected AND inspected positive; both pieces of evidence must be conditioned on. Supplier jade: fr...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Supplier jade", "criteria": null }, { "id": "o1", "name": "Supplier cobalt", "criteria": null }, { "id": "o2", "name": "Supplier silver", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.255170561375235, 0.26000537201181845, 0.4848240666129465 ] }
A robotics workshop receives items from mutually exclusive suppliers. An item first passes a selection filter, then is inspected. Given its supplier, selection and a positive inspection are independent. The observed item was selected AND inspected positive; both pieces of evidence must be conditioned on. Supplier amber...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Supplier ochre", "criteria": null }, { "id": "o1", "name": "Supplier amber", "criteria": null } ]
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.8181818181818182, 0.18181818181818182 ] }
At a sports club, a missing item is located in exactly one of four bins: jade, silver, cedar, or ochre. Two inspectors each issued a report, and both reports were positive. The prior probabilities for the item's location are as follows: bin cedar (5/16), bin jade (1/16), bin ochre (1/16), and bin silver (9/16). The pro...
What is the conditional probability distribution over the listed possibilities?
[ { "id": "o0", "name": "Item is in bin jade", "criteria": null }, { "id": "o1", "name": "Item is in bin silver", "criteria": null }, { "id": "o2", "name": "Item is in bin cedar", "criteria": null }, { "id": "o3", "name": "Item is in bin ochre", "criteria": ...
probabilistic_reasoning
choice
null
{ "kind": "soft", "probabilities": [ 0.014134275618374558, 0.7359919232710752, 0.21453811206461385, 0.0353356890459364 ] }
End of preview. Expand in Data Studio

Dataset Card for OpenJevData-140k

Dataset Summary

OpenJevData-140k is a curated release of the data collection used to train OpenJev-4B. It contains 146,738 decision-making examples across 19 task categories, organized into SFT and RL splits.

Each example presents a state, a question, and a request-specific set of natural-language options. The data include hard answers and soft probability distributions, with candidate sets ranging from 2 to 77 options. Languages are English and Chinese.

Data Splits

The SFT split contains 100,345 examples for supervised fine-tuning: 86,023 hard and 14,322 soft examples. The RL split contains 46,393 examples for reinforcement learning: 28,667 hard and 17,726 soft examples. Together they provide 146,738 examples.

Task Distribution

OpenJevData-140k task distribution by SFT and RL split

  • Probabilistic reasoning: Infer outcome probabilities from uncertainty, conditional information, sampling, or noisy evidence.
  • Deductive reasoning: Derive conclusions from stated premises, rules, or natural-language entailment.
  • Commonsense context: Use everyday knowledge to answer a question or select a plausible continuation.
  • Knowledge QA: Answer factual and subject-specific questions across multiple domains.
  • Policy exceptions: Apply policies while resolving exceptions, rule precedence, and conflicting conditions.
  • Multi-hop reasoning: Connect facts across passages, documents, or entities to reach an answer.
  • Temporal / numeric: Apply rules involving dates, durations, numeric thresholds, or time-dependent conditions.
  • Quantitative reasoning: Solve numerical questions involving arithmetic, word problems, financial information, or tables.
  • Intent routing: Identify the user intent and select an appropriate tool, route, or action.
  • Evidence validation: Check whether evidence supports a claim or whether a response meets stated semantic and format requirements.
  • Reading comprehension: Answer questions using information stated or implied in a supplied passage.
  • Answer preference: Choose the response that best satisfies the request among candidate answers.
  • Option logic: Jointly interpret logical statements and dependencies distributed across the candidate options.
  • Score quality: Assign a rating for qualities such as helpfulness, coherence, clarity, or preference strength.
  • Score rubrics: Assign a score by applying explicit criteria for completeness, coverage, compliance, or task completion.
  • Constraint planning: Choose an action or plan that satisfies interacting constraints and trade-offs.
  • Code / database: Reason about code behavior or select the database query that answers a request.
  • Emotion recognition: Identify the emotion conveyed by a piece of text.
  • Score intensity: Rate the strength of a tone or the severity of an impact on an ordered scale.

Dataset Creation

The source benchmarks include ARC, BANKING77, BoolQ, CodeContests, CommonsenseQA, ConditionalQA, ContractNLI, FinQA, GoEmotions, HellaSwag, HelpSteer2, HoVer, LogiQA 2.0, MASSIVE, MathQA, MMLU auxiliary data, MultiDoc2Dial, MuSiQue, OpenBookQA, OR-ShARC, PRM800K, QASC, RAGTruth, RuleTaker, SNLI, Spider, TAT-QA, TempReason, TimeQA, ToolBench, WANLI, and When2Call, together with instruction-following constraint datasets and human-annotated ratings. These sources are converted into a shared decision format and complemented by program-generated tasks and LLM-assisted synthesis. Labels come from source annotations, executable checks, exact probability calculations, or reviewed judgments, depending on the task.

Synthetic data generation uses the input token-length characteristics of JevBench Public as a reference to broaden input-length coverage. The collection includes both short, straightforward questions and longer, more demanding decision problems. The harder tasks include multi-step reasoning, interacting rules and exceptions, cross-option logic, temporal and quantitative constraints, and decisions under uncertainty.

Data Format

Each example contains the following fields:

  • state: context, evidence, rules, or a scenario.
  • question: the requested decision.
  • options: an ordered list of {id, name, criteria} objects. Nullable criteria may contain essential conditions and is part of the model input.
  • category: the broad task category.
  • task: choice, score, or noul; each uses the supplied candidate options.
  • score_values: numeric values aligned with the options for scoring tasks, otherwise null.
  • answer: {kind, probabilities}, where kind is hard or soft. The probabilities align by position with options and sum to one. A hard answer is represented by a one-hot distribution.

Loading the Dataset

from datasets import load_dataset

dataset = load_dataset("shenjunhao/OpenJevData-140k")
sft = dataset["SFT"]
rl = dataset["RL"]

print(len(sft), len(rl))  # 100345 46393
example = sft[0]
options = example["options"]
gold_probabilities = example["answer"]["probabilities"]

Licensing Information

MIT applies to the original contributions in this release. Adapted source material retains its upstream license and attribution requirements; see SOURCE_NOTICES.md.

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