A) \[\frac{3}{8}\]
B) \[\frac{1}{5}\]
C) \[\frac{3}{4}\]
D) None of these
Correct Answer: A
Solution :
Let \[E\] denote the event that a six occurs and \[A\] the event that the man reports that it is a ?6?, we have \[P(E)=\frac{1}{6},\,\,P({E}')=\frac{5}{6},\,\,P(A/E)=\frac{3}{4}\] and \[P(A/{E}')=\frac{1}{4}\] From Baye?s theorem, \[P(E/A)=\frac{P(E).P(A/E)}{P(E).P(A/E)+P({E}').P(A/{E}')}\] \[=\frac{\frac{1}{6}\times \frac{3}{4}}{\frac{1}{6}\times \frac{3}{4}+\frac{5}{6}\times \frac{1}{4}}=\frac{3}{8}.\]You need to login to perform this action.
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