Question

A husband and wife appear in an interview for two vacancies in the same post. The probability of husband's selection is 1/7 and that of wife's is 1/5. What is the probability that only one of them will be selected?

• A. $\frac{2}{7}$
• B. $\frac{1}{35}$
• C. $\frac{24}{25}$
• D. $\frac{11}{35}$

Answer 1

The correct option is A $\frac{2}{7}$

$A:Husbandselected$

$B:Wifeselected$

$P\left(A\right)=\frac{1}{7}\Rightarrow P\left(\overline{A}\right)=1-P\left(A\right)=1-\frac{1}{7}=\frac{6}{7}$

$P\left(B\right)=\frac{1}{5}\Rightarrow P\left(\overline{B}\right)=1-P\left(B\right)=1-\frac{1}{5}=\frac{4}{5}$

$P\left(onlyoneofthemwillbeselected\right)$

$=P\left(A\right)\times P\left(\overline{B}\right)+P\left(B\right)P\left(\overline{A}\right)$

$=\frac{1}{7}\left(\frac{4}{5}\right)+\frac{1}{5}\left(\frac{6}{7}\right)=\frac{4+6}{35}=\frac{10}{35}=\frac{2}{7}$