$\begin {array} {1 1} (1)\;\large\frac{3}{8} & \quad (2)\;\large\frac{3}{4} \\ (3)\;\large\frac{1}{5} & \quad (4)\;None\: of \: these \end {array}$

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If E denote the event that five occurs and A the event

that the man reports that it is five.

$ P(E)= \large\frac{1}{6}$

$ P(E')= \large\frac{5}{6}$

$ P(A/E)= \large\frac{3}{4}\: \: \: \: P(A/E')= \large\frac{1}{4}$

$ \therefore $ By Baye's theorem

$ P(E/A) = \large\frac{\large\frac{1}{6} \times \large\frac{3}{4}}{\large\frac{1}{6} \times \large\frac{3}{4} + \large\frac{5}{6} \times \large\frac{1}{4}}$

$ = \large\frac{3}{8}$

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