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, P (A) = \[\frac{1}{7}\] and + P (B) = \[\frac{1}{5}\] \[\therefore \] \[P(\overline{A})=\left( 1-\frac{1}{7} \right)=\frac{6}{7}\,\,and\,\,P\,(\overline{B})\,=\left( 1-\frac{1}{5} \right)=\frac{4}{5}\] \[\therefore \] Required probability = P [(A and not B) or (B and not A)] \[\text{= }P\left[ A\text{ }and\text{ }\overline{B} \right)\,\,or\,\,\left( B\text{ }and\text{ }\overline{A} \right)]\] \[=\text{ }P\left[ A\text{ }and\text{ }B \right)+P\text{ }\left( B\text{ }and\text{ }A \right)]\] \[=P(A).P(\overline{B})+P(B)\,.\,P(\overline{A})=\left( \frac{1}{7}\times \frac{4}{5} \right)+\left( \frac{1}{5}\times \frac{6}{7} \right)=\frac{10}{35}=\frac{2}{7}.\]
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