# A speaks tr

Given:

A speaks truth in 75% of cases

B speaks truth in 80% of cases

Now,

P(TA) = P(A speaking truth) = 0.75

P(NA) = P(A not speaking truth) = 1-0.75

P(NA) = 0.25

P(TB) = P(B speaking truth) = 0.80

P(NB) = P(B not speaking truth) = 1-0.80

P(NB) = 0.20

We need to find the probability for case in which A and B contradict each other for narrating an incident.

This happens only when A not telling truth while B is telling truth and vice-versa.

P(CAB) = P(A and B contradict each other)

P(CAB) = P(A tells truth and B doesn’t) + P(B tells truth and A doesn’t)

Since the speaking of A and B are independent events their probabilities will multiply each other.

P(CAB ) = (P(TA)P(NB)) + (P(NA)P(TB))

P(CAB) = (0.75×0.20) + (0.25×0.80)

P(CAB) = 0.15 + 0.20

P(CAB) = 0.35

The required probability is 0.35.

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