Question

Sonal and Meenal appear in an interview for same post having two vacancies. If $\frac 17$ is Sonal's probability of selection and $\frac15$ is Meenal's probability of selection then what is the probability that only one of them is selected?

• A. $\frac17$
• B. $\frac27$
• C. $\frac35$
• D. $\frac15$

Answer 1

Answer: (B)

$\frac27$

Answer 2

Given:
$P(S) = \frac{1}{7}$
$P(M) = \frac{1}{5}$
We need to find the probability that only one of them is selected. There are two cases for this:
1. Sonal is selected, and Meenal is not selected.
2. Meenal is selected, and Sonal is not selected.
The probability that Sonal is selected and Meenal is not selected:
$P(S \text{ and } \neg M) = P(S) \times (1 - P(M))$
$= \frac{1}{7} \times \left(1 - \frac{1}{5}\right)$
$= \frac{1}{7} \times \frac{4}{5}$
$= \frac{4}{35}$
The probability that Meenal is selected and Sonal is not selected:
$P(M \text{ and } \neg S) = P(M) \times (1 - P(S))$
$= \frac{1}{5} \times \left(1 - \frac{1}{7}\right)$
$= \frac{1}{5} \times \frac{6}{7}$
$= \frac{6}{35}$
The total probability that only one of them is selected is the sum of the two probabilities:
$P(\text{only one is selected}) = P(S \text{ and } \neg M) + P(M \text{ and } \neg S)$
$= \frac{4}{35} + \frac{6}{35}$
$= \frac{10}{35}$
$= \frac{2}{7}$
Thus, the correct answer is:
B. 2/7