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Question

Two persons, whose probabilities of speaking the truth are 23 and 56 respectively, assert that a specified ticket has been drawn out of a bag containing 15 tickets. What is the probability of the truth of the assertion?

Solution
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probability of P1 saying false=123=13
probability of P2 saying false=156=16
Probability of truth =bothP1,P2truth(bothP1,P2truth)+(P1false,P2true)+(P1true,P2false)+(bothP1,P2false)
=23×5623×56+13×16+23×16+13×16
=57

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