A man and his wife appeared for an interview for the two vacancies. If the probability of husband's selection is $\frac{1}{3}$ and the probability of wife's selection is $\frac{1}{5}$, then the probability that none of them will be selected?

$\frac{8}{15}$

The correct answer is Option (2) → $\frac{8}{15}$

Let’s solve it step by step.

Given:

• Probability of husband’s selection = $\frac{1}{3}$
• Probability of wife’s selection = $\frac{1}{5}$

Step 1: Probability that husband is not selected

$1 - \frac{1}{3} = \frac{2}{3}$

Step 2: Probability that wife is not selected

$1 - \frac{1}{5} = \frac{4}{5}$​

Step 3: Probability that none of them is selected

(Assuming selections are independent)

$\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$