Question

A and B appeared for an interview for two posts. The probability of A's rejection is $\frac{2}{5}$ and that of B's selection is $\frac{4}{7}$. The probability that one of them is selected, is

• A. $\frac{17}{35}$
• B. $\frac{16}{35}$
• C. $\frac{18}{35}$
• D. None of these

Answer 1

The correct option is A $\frac{17}{35}$

Given,

Probability of A's rejection $P^{\prime }\left(A\right)=\frac{2}{5}$

Probability of A's selection $P\left(A\right)=1-P^{\prime }\left(A\right)=1-\frac{2}{5}=\frac{3}{5}$

Probability of B's selected $P\left(B\right)=\frac{4}{7}$

Probability of B's rejection $P^{\prime }\left(B\right)=1-\frac{4}{7}=\frac{3}{7}$

Probability that one of them is selected $P=P\left(A\right).P^{\prime }\left(B\right)+P^{\prime }\left(A\right).P\left(B\right)=\frac{3}{5}\times \frac{3}{7}+\frac{2}{5}\times \frac{4}{7}$

$=\frac{9}{35}+\frac{8}{35}=\frac{17}{35}$

Hence the probability that one of them is selected $=\frac{17}{35}$