Question

A man and his wife appear for an interview for two posts. The probability of the man's selection is $\frac{1}{5}$ and that of his wife selection is $\frac{1}{7}$. The probability that at least one of them is selected, is:

• A. $\frac{9}{35}$
• B. $\frac{12}{35}$
• C. $\frac{2}{7}$
• D. $\frac{11}{35}$

Answer 1

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

The probability of mans selection is $\frac{1}{5}$.

The probability that man does not select is $1-\frac{1}{5}=\frac{4}{5}$.

The probability of his wife selection is $\frac{1}{7}$.

The probability that mans wife does not select is $1-\frac{1}{7}=\frac{6}{7}$.

The probability that at least one of them is selected is $\frac{1}{5}\times \frac{1}{7}+\frac{1}{5}\times \frac{6}{7}\times \frac{1}{7}\times \frac{4}{5}=\frac{11}{35}$.

Therefore the correct option is $D$.