Question:hard

A man and his wife appear in an interview for two vacancies in the same post. The probability of husband's selection is (1/7) and the probability of wife's selection is (1/5). What is the probability that only one of them is selected ?

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For any two independent events with probabilities \(p_1\) and \(p_2\):
The probability that exactly one occurs is:
\[ P = p_1(1-p_2) + p_2(1-p_1) \]
Here: \(\frac{1}{7}\left(\frac{4}{5}\right) + \frac{1}{5}\left(\frac{6}{7}\right) = \frac{4+6}{35} = \frac{10}{35} = \frac{2}{7}\).