# 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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