Question

A man and his wife appear for an interview for two vacancies in the same posts. The probability of the husband’s selection is 1/7 and that of the wife’s selection is 1/5. What is the probability that only one of them will be selected

• A. $\frac{1}{7}$
• B. $\frac{2}{7}$
• C. $\frac{3}{7}$
• D. None of these

Answer 1

The correct option is B

$\frac{2}{7}$

Explanation for correct option:

Option (B): $\frac{2}{7}$

Since, Probability = $\frac{Favorableoutcomes}{Totalnumberofoutcomes}$

Let, A = The event that the husband is selected

B = The event that the wife is selected

Given,

P(A) = $\frac{1}{7}$

P(B) = $\frac{1}{5}$

Probability of husband not getting selected P(A') = $1-\frac{1}{7}$

= $\frac{6}{7}$

Probability of the wife not getting selected P(B') = $1-\frac{1}{5}$

= $\frac{4}{5}$

Probability of any one of them getting selected = P(A) * P(B') $+$P(B) * P(A')

= $\left(\frac{1}{7}\right).\left(\frac{4}{5}\right)+\left(\frac{1}{5}\right).\left(\frac{6}{7}\right)$

= $\left(\frac{4}{35}\right).\left(\frac{6}{35}\right)$

= $\frac{10}{35}$

= $\frac{2}{7}$

Therefore, the probability of only one of them getting selected is $\frac{2}{7}$.

Explanation for incorrect options:

Option (A): $\frac{1}{7}$

Here, the probability of either the husband or his wife getting selected = $\frac{2}{7}$

Therefore, the probability of only one of them getting selected is not$\frac{1}{7}$.

Option (C): $\frac{3}{7}$

Here, the probability of either the husband or his wife getting selected = $\frac{2}{7}$

Therefore, the probability of only one of them getting selected is not$\frac{3}{7}$.

Option (D): None of these

Here, the probability of either the husband or his wife getting selected = $\frac{2}{7}$

Therefore, the probability of only one of them getting selected is one of these.

Hence, Option (B) is the correct answer.