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MMLU-Pro / 8845 / A court is investigating the possible occurrence of an unlikely event T. The…

Problem

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question

A court is investigating the possible occurrence of an unlikely event T. The reliability of two independent witnesses called Alf and Bob is known to the court: Alf tells the truth with probability \alpha and Bob with probability \beta, and there is no collusion between the two of them. Let A and B be the events that Alf and Bob assert (respectively) that T occurred, and let \tau=P(T). What is the probability that T occurred given that both Alf and Bob declare that T occurred? Suppose \alpha=\beta=9/10 and \tau=1/1000. Return the answer up to the thousands decimal.

category

math

options

  1. 0.120
  2. 0.082
  3. 0.001
  4. 0.025
  5. 0.050
  6. 0.075
  7. 0.100
  8. 0.150
  9. 0.200
  10. 0.010

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8845
task_id
8f60915a-f3b2-53d6-8852-a5480282593f
task_key
default--test--8845
task_revision_id
1
config / split
default / test

Official source

initial import