The probability that A speaks truth is 4/5 while this probability for B is 3/4. The probability that they contradict each other when asked to speak on a fact is

Solution :

Given, probabilities of speaking truth are

P(A) = \(4\over 5\) and P(B) = \(3\over 4\)

And their corresponding probabilities of not speaking truth are

P(A’) = \(1\over 5\)  and P(B’) = \(1\over 4\)

The probability that they contradict each other

= P(A).P(B’) + P(B).P(A’)

= \(4\over 5\) \(\times\) \(1\over 4\) + \(1\over 5\) \(\times\) \(3\over 4\)

= \(7\over 20\)

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