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Question

A speaks the truth 8 times out of 10 times. A die is tossed. He reports that it was 5. What is the probability that it was actually 5?

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Solution


Let A denote the event that man reports that 5 occurs and E the event that 5 actually turns up.

∴ P(E) = 16 and PE=1-16=56

Also, PAE = Probability that man reports that 5 occurs given that 5 actually turns up = Probability of man speaking the truth = 810=45

PAE = Probability that man reports that 5 occurs given that 5 doesnot turns up = Probability of man not speaking the truth = 1-45=15

∴ Required probability = PEA=PEPAEPEPAE+PEPAE=16×4516×45+56×15=49

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