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Question

A man is known to speak truth is 75% cases. If he throws an unbiased die and tells his friend that it is a six, then the probability that it is actually a six, is

A
16
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B
18
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C
34
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D
38
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Solution

The correct option is D 38
Let E denote the event that a six occurs and A be the event theat the man reports that it is a six. We have P(E)=16,P(E)=56,P(AE)=34 and P(AE)=14. By Baye’s theorem
P(EA)=P(E).P(AE)P(E).P(AE)+P(E).P(AE)=(16)(34)(16)(34)+(56)(14)=38

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