Question

Brother and sister both appear for an interview. The probability of the selection of brother is $\frac{1}{8}$ while the probability of rejection of sister is $\frac{4}{5}$. What is the probability that only one of them is selected ?

Accepted Answer

A. $P(	ext{Brother selected}) = \frac{1}{8}$, $P(	ext{Brother rejected}) = \frac{7}{8}$. $P(	ext{Sister rejected}) = \frac{4}{5}$, $P(	ext{Sister selected}) = \frac{1}{5}$. $P(	ext{Only one selected}) = P(	ext{Brother selected})P(	ext{Sister rejected}) + P(	ext{Brother rejected})P(	ext{Sister selected})$ $= \left(\frac{1}{8}ight)\left(\frac{4}{5}ight) + \left(\frac{7}{8}ight)\left(\frac{1}{5}ight) = \frac{4}{40} + \frac{7}{40} = \frac{11}{40}$.

Interview selection probability

Explanation

Practise this under exam conditions