A man and his wife appear for an interview for two posts. The probability of the husband’s selection is 1/7 and that of the wife’s selection is 1/5 . - Mathematics and Science MCQ UPTET Paper 2 (Maths & Science) 2026 | ExamTest.live

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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} . What is the probability that only one of them will be selected?

Solution & Step-by-step Explanation

Let H be the event that the husband is selected, and W be the event that the wife is selected.Given: P (H) = \frac{1}{7} ⟹ P (H^{'}) = 1 - \frac{1}{7} = \frac{6}{7} P (W) = \frac{1}{5} ⟹ P (W^{'}) = 1 - \frac{1}{5} = \frac{4}{5} The event "only one of them is selected" means either (Husband is selected AND Wife is not) OR (Husband is not selected AND Wife is selected): P (only one) = [P (H) \times P (W^{'})] + [P (H^{'}) \times P (W)] P (only one) = (\frac{1}{7} \times \frac{4}{5}) + (\frac{6}{7} \times \frac{1}{5}) P (only one) = \frac{4}{35} + \frac{6}{35} = \frac{10}{35} = \frac{2}{7}

Try it yourself before checking the explanation above.

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} . What is the probability that only one of them will be selected?

\frac{1}{7}

\frac{2}{7}

\frac{2}{5}

\frac{1}{5}

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