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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 $P(H) = 1/7$ and $P(W) = 1/5$.The probabili

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$2/7$

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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 $P(H) = 1/7$ and $P(W) = 1/5$.The probability that the husband is not selected is $P(H') = 1 - 1/7 = 6/7$.The probability that the wife is not selected is $P(W') = 1 - 1/5 = 4/5$.The probability that only one of them is selected is $P(H \cap W') + P(H' \cap W)$.Since the events are independent,this is $P(H) 	imes P(W') + P(H') 	imes P(W)$.$= (1/7 	imes 4/5) + (6/7 	imes 1/5) = 4/35 + 6/35 = 10/35 = 2/7$.

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

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