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A man speaks truth 3 times out of 5. He says that in tossing 6 coins, two tails appear so what is the probability that this event is actually true ?

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Let E represents the statement of a person. 

Now, S1 is the event of getting 2 heads and S2 is the event of not getting 2 heads on tossing 6 coins

Now, Probability of statement to be truth if 2 heads are obtained on tossing of 6 coins

P(E/S1) = 3/5

∵ Person speaks truth 3 times out of 5.

Similarly, Probability of statement to be not truth if 2 heads are obtained on tossing of 6 coins

Now, the probability that this event is actually true,

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