A husband and wife appear in an interview for two vacancies for t… - Vidyadip

Question

A husband and wife appear in an interview for two vacancies for the same post. The probability of husband's selection is $\frac{1}{7}$ and that of wife's selection is $\frac{1}{5}$. What is the probability that,
None of them will be selected?

✓

Answer

Given, Probability of Husband's (H) selection $=\frac{1}{7}$
$\text{P(H)}=\frac{1}{7}$
Probability of Wife's (W) selection $=\frac{1}{5}$
$\text{P(W)}=\frac{1}{5}$
P(None of them selected)
$=(\overline{\text{H}}\cap\overline{\text{W}})$
$=\text{P}(\overline{\text{H}})\text{ P}(\overline{\text{W}})$
$=(1-\text{P(H)})(1-\text{P(W)})$
$=\Big(1-\frac{1}{7}\Big)\Big(1-\frac{1}{5}\Big)$
$=\frac{6}{7}\times\frac{4}{5}$
$=\frac{24}{35}$
Required probability $=\frac{24}{35}$

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