Question

$A$ and $B$ are seeking admission into $IIT$. If the probability for $A$ to be selected is $0.5$ and that both to be selected is $0.3$, them is it possible that, the probability of $B$ to be selected is $0.9$?

Answer 1

Given that probability of $A$ is $P\left(A\right)=0.5$

and probability that both $A$ and $B$ to be selected is $P(A\cap B)=0.3$

We know that $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$⟹1=0.5+P\left(B\right)-0.3$

$⟹1=0.2+P\left(B\right)$

$⟹P\left(B\right)=0.8$

Therefore, $P\left(B\right)$ cannot be $0.9$