Question

$A$ is interviewed for $3$ posts. There are $4$ candidates for post $1,3$ for second post and $5$ for post No. three. the probability of $A$'s being selected for none of the posts is:

• A. $\frac{3}{4}$
• B. $\frac{2}{5}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

Answer 1

The correct option is B $\frac{2}{5}$

Let $P\left(A\right)=$ Probability of getting first company by the candidates.

Similarly, $P\left(B\right)$ $\xi$ $P\left(C\right)$ be the probability of getting into second and third company respectively.

$\Rightarrow P(A\cup B\cup C)=P\left(A\right)+P\left(B\right)+P\left(C\right)-P(A\cap B)-P(A\cap C)-P(B\cap C)+P(A\cap B\cap C)$

$\Rightarrow P(A\cup B\cup C)=\frac{1}{4}+\frac{1}{3}+\frac{1}{5}-(\frac{1}{4}\times \frac{1}{3})-(\frac{1}{4}\times \frac{1}{5})-(\frac{1}{3}\times \frac{1}{5})+(\frac{1}{34}\times \frac{1}{3}\times \frac{1}{5})$

$=\frac{1}{4}+\frac{1}{3}+\frac{1}{5}-\frac{1}{12}-\frac{1}{20}-\frac{1}{15}+\frac{1}{60}$

$=\frac{3}{5}.$

$\Rightarrow P$ ( not getting selected for none of the post ) $=1-\frac{3}{5}$

$=\frac{2}{5}$

Hence, the answer is $\frac{2}{5}.$