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(B) Let $H$ be the event that the husband is selected and $W$ be the event that the wife is selected.Given: $P(H) = \frac{1}{7}$ and $P(W) = \frac{1}{

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$\frac{2}{7}$

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(B) Let $H$ be the event that the husband is selected and $W$ be the event that the wife is selected.Given: $P(H) = \frac{1}{7}$ and $P(W) = \frac{1}{5}$.Probability that the husband is not selected: $P(H') = 1 - \frac{1}{7} = \frac{6}{7}$.Probability that the wife is not selected: $P(W') = 1 - \frac{1}{5} = \frac{4}{5}$.Only one of them is selected if (husband is selected $AND$ wife is not) $OR$ (wife is selected $AND$ husband is not).Probability = $P(H) 	imes P(W') + P(W) 	imes P(H')$.Probability = $(\frac{1}{7} 	imes \frac{4}{5}) + (\frac{1}{5} 	imes \frac{6}{7})$.Probability = $\frac{4}{35} + \frac{6}{35} = \frac{10}{35} = \frac{2}{7}$.

$A$ 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?

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