MHT CET · Maths · Probability

A man and his wife appear for an interview for two posts. The probability of the husband's selection is \(\frac{1}{7}\). and that of the wife's selection is \(\frac{1}{5}\). If they appear for the interview independently, then the probability that only one of them is selected, is

A \(\frac{1}{7}\)
B \(\frac{2}{7}\)
C \(\frac{6}{7}\)
D \(\frac{4}{7}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{2}{7}\)

Step-by-step Solution

Detailed explanation

The probability of husband is not selected
\(=1-\frac{1}{7}=\frac{6}{7}\)
The probability that wife is not selected
\(=1-\frac{1}{5}=\frac{4}{5}\)
The probability that only husband selected
\(=\frac{1}{7} \times \frac{4}{5}=\frac{4}{35}\)
The probability that only wife selected
\(=\frac{1}{5} \times \frac{6}{7}=\frac{6}{35}\)
\(\begin{aligned}
\text { Hence, required probability } & =\frac{6}{35}+\frac{4}{35}=\frac{10}{35} \\
& =\frac{2}{7}
\end{aligned}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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