Two friends, P and Q, appeared in an interview for two vacancies for the same post. The probability of P's selection is \(\frac{1}{3}\) and that of Q's selection is \(\frac{2}{7}\). What is the probability that at least one of them will be selected?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{11}{21}\)
“At least one is selected” fails only when neither is selected, so its probability is \(1-P(\text{neither})\). The two selections are independent, so the probabilities of rejection are multiplied.
P not selected: \(\displaystyle 1-\frac{1}{3}=\frac{2}{3}\)
Q not selected: \(\displaystyle 1-\frac{2}{7}=\frac{5}{7}\)
Neither selected: \(\displaystyle \frac{2}{3}\times\frac{5}{7}=\frac{10}{21}\)
At least one selected: \(\displaystyle 1-\frac{10}{21}=\frac{11}{21}\)