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 at least one of them will be selected?

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

Answer 1

The correct option is D $\frac{11}{35}$

$P\left(atleastoneofthemwillbeselected\right)$

$=1-\left[P\right(\overline{A})\times P(\overline{B}\left)\right]$

$=1-(\frac{6}{7}\times \frac{4}{5})=1-\frac{24}{35}=\frac{11}{35}$