JEE Main 2022 (Online) 25th July Evening ShiftQuestion 1
If $A$ and $B$ are two events such that $P(A)=\frac13$, $P(B)=\frac15$ and $P(A\cup B)=\frac12$, then $P(A|B')+P(B|A')$ is equal to
Probability
Solution
$P(A\cap B)=\frac13+\frac15-\frac12=\frac1{30}$. $P(A|B')=\frac{P(A)-P(A\cap B)}{1-P(B)}=\frac{3/10}{4/5}=\frac38$. $P(B|A')=\frac{P(B)-P(A\cap B)}{1-P(A)}=\frac{1/6}{2/3}=\frac14$. Sum $=\frac58$. Answer: (B).