Question

A man and woman appear in an interview for two vacancies in the same post. The probability of the man’s selection is ¼ and that of the woman’s selection is 1/3. What is the probability that none of them will be selected

• A. $\frac{1}{2}$
• B. $\frac{1}{12}$
• C. $\frac{1}{4}$
• D. None of these

Answer 1

The correct option is A

$\frac{1}{2}$

Explanation for correct option:

Option (A): $\frac{1}{2}$

Let A = event that the man will be selected

B = event that the woman is selected.

Given, P(A) = $\frac{1}{4}$

P(B) = $\frac{1}{3}$

Probability of the man not getting selected P(A') = $1-\frac{1}{4}$

= $\frac{3}{4}$

Probability of the woman not getting selected P(B') = $1-\frac{1}{3}$

= $\frac{2}{3}$

Probability that none of them is going to be selected = P(A').P(B')

= $\frac{3}{4}\times \frac{2}{3}$

= $\frac{1}{2}$

Therefore, the probability that none of them will be selected is $\frac{1}{2}$.

Explanation for incorrect options:

Option (B): $\frac{1}{12}$

Here, the probability that none of the husband and wife is selected = $\frac{1}{2}$

Therefore, the probability that none of them is selected is not $\frac{1}{12}$.

Option (C): $\frac{1}{4}$

Here, the probability that none of the husband and wife is selected = $\frac{1}{2}$

Therefore, the probability that none of them is selected is not $\frac{1}{4}$

Option (D): None of these

Here, the probability that none of the husband and wife is selected = $\frac{1}{2}$

Therefore, the probability that none of them is selected is one of these.

Hence, Option (A) is the correct answer.