Question

$A$ and $B$ are two candidates seeking admission in I.I.T. The probability that $A$ is selected is $0.5$ and the probability that both $A$ and $B$ are selected is atmost $0.3$. Is it possible that the probability of $B$ getting selected is $0.9$? If it is possible then enter 1, else enter 0.

Answer 1

If we have $P\left(B\right)=0.9$ ,then we will get $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=0.5+0.9-0.3=1.1>1$
Hence, this is not possible.