Question

A husband and a wife appear in an interview for two vacancies in the same post. The probability of husband`s selection is $\frac{1}{7}$ and that of wife's selection is $\frac{1}{5}$. What is the probability that only one of them will be selected?

• A. $\frac{1}{7}$
• B. $\frac{2}{7}$
• C. $\frac{3}{7}$
• D. $\frac{4}{7}$

Answer 1

The correct option is B $\frac{2}{7}$

There would be three cases.

1. Husband is selected while wife doesn't get selected.

2. Wife is selected while husband doesn't get selected.

3. Both of them get selected.

Probability of husband not to get selected $=\frac{6}{7}$

Probability of wife not to get selected $=\frac{4}{5}$

Probability only one to get selected $=\frac{6}{7}\times \frac{1}{5}+\frac{1}{7}\times \frac{4}{5}$

$=\frac{10}{35}=\frac{2}{7}$