Question

A man and a woman appears in an interview for two vacancies in the same post. The probability of mans selection is $\frac{1}{4}$ and that of the womans selection is $\frac{1}{3}$ . What is the probability that none of them will be selected?

• A. $\frac{1}{2}$
• B. $\frac{1}{12}$
• C. $\frac{1}{4}$
• D. None of these

Answer 1

Answer: (A)

Let $E_1$ be the events that man will be selected and $E_2$ the events that woman will be selected.
Then, $P\left(E_1\right)=\frac{1}{4}$
So, $P\left({\bar{E}}_1\right)=1-\frac{1}{4}=\frac{3}{4}$
and $P\left(E_2\right)=\frac{1}{3}$
$\Rightarrow P\left({\bar{E}}_2\right)=\frac{2}{3}$
$\therefore E_1$ and $E_2$ are independent events.
$\therefore P\left({\bar{E}}_1\cap {\bar{E}}_2\right)=P\left({\bar{E}}_1\right)\times P\left({\bar{E}}_2\right)$
$=\frac{3}{4}\times \frac{2}{3}=\frac{1}{2}$