Question

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

• A. $\frac{12}{35}$
• B. $\frac{6}{35}$
• C. $\frac{24}{35}$
• D. $Noneofthese$

Answer 1

The correct option is C $\frac{24}{35}$

P(None of them will be selected)
$=P\left[\right(notE\left)and\right(notF\left)\right]=P(\overline{E}\cup \overline{F})=P\left(\overline{E}\right)\times P\left(\overline{F}\right)=\frac{6}{7}\times \frac{4}{5}=\frac{24}{35}$