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?

$\frac{11}{21}$

The correct answer is Option (2) → $\frac{11}{21}$

Step 1: Given probabilities

• Probability of P being selected: $P(P) = \frac{1}{3}$ ​
• Probability of Q being selected: $P(Q) = \frac{2}{7}$​

We are asked: Probability that at least one of them is selected

$P(\text{at least one}) = P(P \cup Q) = P(P) + P(Q) - P(P)P(Q)$

Step 2: Substitute values

$P(P \cup Q) = \frac{1}{3} + \frac{2}{7} - \left(\frac{1}{3} \times \frac{2}{7}\right)$

$= \frac{7}{21} + \frac{6}{21} - \frac{2}{21} = \frac{11}{21}$