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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 none of them will be selected?
Solution
\[P\left( \text{ husband will be selected } \right) = P\left( A \right) = \frac{1}{7}\]
\[P\left( \text{ wife will be selected } \right) = P\left( B \right) = \frac{1}{5}\]
\[ P\left( \text{ none of them will be selected } \right) = P\left( A \cap B \right)\]
\[ = P\left( \bar{A} \right) \times P\left( \bar{B} \right)\]
\[ = \left( 1 - \frac{1}{7} \right)\left( 1 - \frac{1}{5} \right)\]
\[ = \frac{24}{35}\]
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