CMAT 2020 Solved Question Paper

Let A = Event that the brother is selected
and B = Event that the wife is selected
Then, $\mathit{P}\left(\mathit{A}\right)=\frac{1}{8}$
and $\mathit{P}\left(\overline{\mathit{B}}\right)=45$
∴ $\mathit{P}\left(\overline{\mathit{A}}\right)=1-\mathit{P}\left(\mathit{A}\right)$
$=1-\frac{1}{8}=\frac{7}{8}$
and $\mathit{P}\left(\mathit{B}\right)=1-\mathit{P}\left(\overline{\mathit{B}}\right)$
$=1-\frac{4}{5}=\frac{1}{5}$
Required probability = Probability that only one of them is selected
= P[(A and not B) or (B and not A)]
= P (A and B) or ( $\overline{\mathit{B}}$ and $\overline{\mathit{A}}$ )
= P(A and $\overline{\mathit{B}}$ ) P(B and $\overline{\mathit{A}}$ )
$=\mathit{P}\left(\mathit{A}\right).\mathit{P}\left(\overline{\mathit{B}}\right)+\mathit{P}\left(\mathit{B}\right).\mathit{P}\left(\overline{\mathit{A}}\right)$
$=\frac{1}{8}\times \frac{4}{5}+\frac{1}{5}\times \frac{7}{8}$
$=\frac{4}{40}+\frac{7}{40}=\frac{4+7}{40}=\frac{11}{40}$