Two persons A and B appear in an interview for two vacancies. If the probabilities of their selections are 1/4 and 1/6 respectively, then the probability that none of them is selected shall be:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{5}{8}\)
The selection of A and that of B are independent events, so the probability that both happen is the product of their probabilities. “None is selected” means A is not selected and B is not selected, and the probability that an event does not happen is \(1-P\).
A not selected: \(\displaystyle 1-\frac{1}{4}=\frac{3}{4}\)
B not selected: \(\displaystyle 1-\frac{1}{6}=\frac{5}{6}\)
Neither selected: \(\displaystyle \frac{3}{4}\times\frac{5}{6}=\frac{15}{24}=\frac{5}{8}\)