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Question: A man is known to speak truth in 75% cases. He throws a dice & reports that it is a six. The probabi...

A man is known to speak truth in 75% cases. He throws a dice & reports that it is a six. The probability that it is actually a six is -

A

38\frac { 3 } { 8 }

B

34\frac { 3 } { 4 }

C

15\frac { 1 } { 5 }

D

None of these

Answer

38\frac { 3 } { 8 }

Explanation

Solution

P = FCTC\frac { \mathrm { FC } } { \mathrm { TC } } = 34⋅1634⋅16+14⋅56\frac { \frac { 3 } { 4 } \cdot \frac { 1 } { 6 } } { \frac { 3 } { 4 } \cdot \frac { 1 } { 6 } + \frac { 1 } { 4 } \cdot \frac { 5 } { 6 } } = 38\frac { 3 } { 8 }