Suppose that \(5 \%\) of men and \(0.25 \%\) of women have gray hair. A gray hair person is selected at random. If there are equal number of males and females, then the probability that the person selected being men is

A grey haired person is selected at eandom, the probability that this person is male \(=\mathrm{P}(\mathrm{M} / \mathrm{G})\) Here \(M\) is men, \(W\) is women, \(G\) is grey hair.
\(
\begin{aligned}
\therefore \mathrm{P}(\mathrm{M} / \mathrm{G}) &=\frac{\mathrm{P}(\mathrm{M}) \times \mathrm{P}(\mathrm{G} / \mathrm{M})}{\mathrm{P}(\mathrm{M}) \times \mathrm{P}(\mathrm{G} / \mathrm{M})+\mathrm{P}(\mathrm{W}) \times \mathrm{P}(\mathrm{G} / \mathrm{W})} \\
&=\frac{\frac{1}{2} \times \frac{5}{100}}{\left(\frac{1}{2} \times \frac{5}{100}\right)+\left(\frac{1}{2} \times \frac{0.25}{100}\right)}=\frac{20}{21}
\end{aligned}
\)