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 ?

Probability of brother's selection = $$\frac{1}{8}$$ and probability of brother's rejection = $$\frac{7}{8}$$

Probability of sister's selection = $$\frac{1}{5}$$ and probability of sister's rejection = $$\frac{4}{5}$$

Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)

= $$(\frac{1}{8})(\frac{4}{5})+(\frac{7}{8})(\frac{1}{5})$$

= $$\frac{4}{40}+\frac{7}{40}=\frac{11}{40}$$

=> Ans - (A)