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

Vedclass · Accepted Answer

$\frac{24}{35}$

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(C) Let $A$ be the event that the husband is selected and $B$ be the event that the wife is selected.Given: $P(A) = \frac{1}{7}$ and $P(B) = \frac{1}{5}$.The probability that the husband is not selected is $P(\bar{A}) = 1 - P(A) = 1 - \frac{1}{7} = \frac{6}{7}$.The probability that the wife is not selected is $P(\bar{B}) = 1 - P(B) = 1 - \frac{1}{5} = \frac{4}{5}$.Since the events are independent,the probability that none of them will be selected is $P(\bar{A} \cap \bar{B}) = P(\bar{A}) 	imes P(\bar{B})$.$P(\bar{A} \cap \bar{B}) = \frac{6}{7} 	imes \frac{4}{5} = \frac{24}{35}$.

$A$ husband and wife appear in an interview for $2$ vacancies in the same post. The probability of husband's selection is $\frac{1}{7}$ and that of wife's is $\frac{1}{5}$. What is the probability that none of them will be selected?

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