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Question

A man is know to speak truth 3 out of 4 times. He throws a dice and reports that it is six. The probability that it is actually six is

A
38
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B
15
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C
35
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D
None of these
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Solution

The correct option is A 38
Let A denotes the event that a six occurs and B the events that the man reports that it is a six.
Then the probability that it is actually a six is given by
P(AB)=P(AB)P(B)
Now P(AB)=16×34=324
P(B)=P(AB)+P(¯¯¯¯AB)=16×34+56×14=824
Hence P(AB)=324824=38

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