Question

Ar a selection, the probability of selection of $A$ is $\frac{1}{7}$ and that of $8$ is $\frac{1}{5}$ . If A and $B$ are independent events, then the probability that neither of them would be selected is ?

Answer 1

$P\left(A\right)=\frac{1}{7}$

and $P\left(B\right)=\frac{1}{5}$

Both are independent events :

$\Rightarrow$ Not selection $\overline{P}\left(A\right)=1-\frac{1}{7}=\frac{6}{7}$

and $\overline{P}\left(B\right)=1-\frac{1}{5}=\frac{4}{5}$

$\Rightarrow$ Probability of both not getting selected $=\frac{6}{7}\times \frac{4}{5}=\frac{24}{35}$

Hence, the answer is $\frac{24}{35}.$