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 only one of them will be selected?

• A. $\frac{5}{7}$
• B. $\frac{1}{5}$
• C. $\frac{2}{7}$
• D. $\frac{2}{35}$

Answer 1

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

P(only one of them will be selected)
$=P\left(\right[EandnotF\left)or\right(FandnotE\left)\right]=P\left[\right(E\cap \overline{F})\cup (F\cap \overline{E}\left)\right]=P\left(E\right)P\left(\overline{F}\right)+P\left(F\right)P\left(\overline{E}\right)=\frac{1}{7}\times \frac{4}{5}+\frac{1}{5}\times \frac{6}{7}=\frac{2}{7}$