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14.Probability
medium
A man and his wife appear for an interview for two posts. The probability of the husband's selection is $\frac{1}{7}$ and that of the wife's selection is $\frac{1}{5}$. What is the probability that only one of them will be selected
A
$\frac{1}{7}$
B
$\frac{2}{7}$
C
$\frac{3}{7}$
D
None of these
Solution
(b) The probability of husband is not selected $ = 1 – \frac{1}{7} = \frac{6}{7}$
The probability that wife is not selected $ = 1 – \frac{1}{5} = \frac{4}{5}$
The probability that only husband selected $ = \frac{1}{7} \times \frac{4}{5} = \frac{4}{{35}}$
The probability that only wife selected $ = \frac{1}{5} \times \frac{6}{7} = \frac{6}{{35}}$
Hence required probability $ = \frac{6}{{35}} + \frac{4}{{35}} = \frac{{10}}{{35}} = \frac{2}{7}$.
Standard 11
Mathematics
