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(D) Let $A$ be the event that the husband is selected and $B$ be the event that the wife is selected.Given: $P(A) = 1/7$ and $P(B) = 1/5$.The probabil

Vedclass · Accepted Answer

$11/35$

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(D) Let $A$ be the event that the husband is selected and $B$ be the event that the wife is selected.Given: $P(A) = 1/7$ and $P(B) = 1/5$.The probability that the husband is not selected is $P(\bar{A}) = 1 - 1/7 = 6/7$.The probability that the wife is not selected is $P(\bar{B}) = 1 - 1/5 = 4/5$.The probability that at least one of them is selected is given by $1 - P(	ext{neither is selected})$.$P(	ext{at least one}) = 1 - P(\bar{A}) 	imes P(\bar{B})$.$P(	ext{at least one}) = 1 - (6/7 	imes 4/5) = 1 - 24/35$.$P(	ext{at least one}) = (35 - 24) / 35 = 11/35$.

$A$ husband and wife appear in an interview for $2$ vacancies in the same post. The probability of the husband's selection is $1/7$ and that of the wife's is $1/5$. What is the probability that at least one of them will be selected?

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