$A$ and $B$ are two candidates seeking admission in IIT. The probability that $A$ is selected is 0.5

Question

$A$ and $B$ are two candidates seeking admission in IIT. The probability that $A$ is selected is 0.5 and the probability that both $A$ and $B$ are selected is atmost 0.3 . The maximum %value of probability of $B$ getting selected is

Professor PC Thomas Classes · Answer

Given $P(A)=0.5$\ and $P(A \cap B) \leq 0.3$\ Now $P(A \cup B)=P(A)+P(B)-P(A \cap B) \leq 1$.\ $\Rightarrow \quad 0.5+P(B)-P(A \cap B) \leq 1$.\ $\Rightarrow P(B) \leq 0.5+P(A \cap \mathrm{~B}) \leq 0.5+0.3$\ $\Rightarrow \quad P(B) \leq 0.8$\ [Using (i)]\ $	herefore P(B)$ is atmost 0.8 . hence $P(B)=0.9$ is false. i.e., $P(B)$ cannot be 0.9 .