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?
Answer & explanation
Correct answer: option 2
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)
$\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$