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qid 8845 · math
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.
- 0.120
- 0.082
- 0.001
- 0.025
- 0.050
- 0.075
- 0.100
- 0.150
- 0.200
- 0.010
Our answer: F. 0.075 Source quote machine-checked (exact quote)
How it was answered
Multi-step solver (maze), replayed by code
Current source
Wikipedia, "Bayes' theorem"
https://en.wikipedia.org/wiki/Bayes%27_theorem
Source quote machine-checked (exact quote)
Earlier version (superseded)
https://en.wikipedia.org/wiki/Bayes%27_theorem
Source weak (http_get_200_text_and_question_terms)
Earlier version (superseded)
No public source has been found for this card yet (3 places checked internally).