The probabilities that and speak the truth independently are and respectively. If they make the same statement, the probability that the statement is indeed true is
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4 marks, −1StatisticsProbability and Bayes' theoremTotal probability and Bayes' theoremModerateabout 2 min
JNU SIS 2012 Question 13: Probability and Bayes' theorem
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The probabilities that A and B speak the truth independently are p and q respectively. If they make the same statement, the probability that the statement is indeed true is (A) pq/(pq + 1/2 (1 - p)(1 + q)) (B) pq/(pq + (1 - p)(1 - q)) (C) pq/(pq + (1 - p)(1 + q)) (D) 2pq/(pq + (1 - p)(1 + q))
Probability and Bayes' theorem has come up 190 times in 7 exams since 2004.
What this question tests
This question is on Total probability and Bayes' theorem, part of Probability and Bayes' theorem in Statistics.
Reversing a conditional probability and updating beliefs from evidence.
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