A) \[\frac{4}{5}\]
B) \[\frac{2}{7}\]
C) \[\frac{8}{15}\]
D) \[\frac{4}{7}\]
E) None of these
Correct Answer: B
Solution :
Explanation Option [b] is correct. Let A == Event that the husband is selected And B = Event that the wife is selected. Then, \[\operatorname{P}\left( A \right)=\frac{1}{7}\]and \[\operatorname{P}\left( B \right)=\frac{1}{5}\] \[\therefore P(\overline{A})=\left( 1-\frac{1}{7} \right)=\frac{6}{7}and\,P(\overline{B})=\left( 1-\frac{1}{5} \right)=\frac{4}{5}\] \[\therefore \] Required probability = P [(A and not B) or (B and not A)] \[=P\,\,[(A\,and\,\overline{B}\,)or\,(B\,\,and\,\overline{A})]\] \[=P\,\,[(A\,and\,\overline{B}\,)+\operatorname{P}\,(B\,\,and\,\overline{A})]\] \[=\,P\,(A).P(\overline{B})+P(B).P(\overline{A})=\left( \frac{1}{7}\times \frac{4}{5} \right)+\left( \frac{1}{5}\times \frac{6}{7} \right)=\frac{10}{35}=\frac{2}{7}.\]
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