A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

Let us consider some samples,

A: man speaks truth

B: man lies

E: six on the die

Now,

The probability of the samples are

P(A) =

P(B)=1 - P(A)

P(B)=

P(B)=

P(E|A)=

And,

P(E|B)=1 - P(E|A)

P(E|B)=

P(E|B)=

We have to Find the probability that is actually a six , if the men speaks that it is a six

So that, we have to find : P(A|E)

Hence, The required probability is 3/8.