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) → \(\frac{8}{15}\)
The selection of the husband and that of the wife are independent events, so the probability that both things happen is the product of their probabilities. “None selected” means the husband is not selected and the wife is not selected.
Husband not selected: \(1-\frac{1}{3}=\frac{2}{3}\)
Wife not selected: \(1-\frac{1}{5}=\frac{4}{5}\)
Neither selected: \(\displaystyle \frac{2}{3}\times\frac{4}{5}=\frac{8}{15}\)