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 ?

 

Answer 1

\[P\left( \text{ husband will be selected }  \right) = P\left( A \right) = \frac{1}{7}\]

\[P\left( \text{ wife will be selected }  \right) = P\left( B \right) = \frac{1}{5}\]

\[P\left( \text{ only one of them will be selected } \right) = P\left( A \right)P\left( \bar{B} \right) + P\left( \bar{A} \right)P\left( B \right)\]

\[ = \frac{1}{7}\left( 1 - \frac{1}{5} \right) + \frac{1}{5}\left( 1 - \frac{1}{7} \right)\]

\[ = \frac{4}{35} + \frac{6}{35}\]

\[ = \frac{10}{35}\]

\[ = \frac{2}{7}\]