A man is known to speak truth 3 out of 4 times. He throws a die and report that it is a 6. Find the probability that it is actually 6.

Explanation

Given :
A man is known to speak truth three
out of four times.
He throws a die and observe that it is a 6.
Probability that the man speaks the truth is `P(A)=3/4`
The probability that the man lies is `P(B)=1−P(A)=1-3/4`
`=1/4`
probability of getting `6` is `1/6`
probability of not getting `6= 1-1/6 =5/6`
`P(A/B)=(P(B/A)*P(A))/(P(B))`
Applying Bayes’ theorem, we get the required probability ,
`=(1/6xx3/4)/(1/6xx3/4+5/6xx1/4)=3/8`
Hence, the probability that it is actually a `6 =3/8`
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