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Question
A husband and wife appear in an interview for two vacancies for the same post. The probability of husband's selection is 1/7 and that of wife's selection is 1/5. What is the probability that only one of them will be selected ?
Solution
\[P\left( \text{ husband will be selected } \right) = P\left( A \right) = \frac{1}{7}\]
\[P\left( \text{ wife will be selected } \right) = P\left( B \right) = \frac{1}{5}\]
\[P\left( \text{ only one of them will be selected } \right) = P\left( A \right)P\left( \bar{B} \right) + P\left( \bar{A} \right)P\left( B \right)\]
\[ = \frac{1}{7}\left( 1 - \frac{1}{5} \right) + \frac{1}{5}\left( 1 - \frac{1}{7} \right)\]
\[ = \frac{4}{35} + \frac{6}{35}\]
\[ = \frac{10}{35}\]
\[ = \frac{2}{7}\]
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