JEE Main 2025 (Online) 8th April Evening ShiftQuestion 1
If $A$ and $B$ are two events such that $P(A)=0.7$, $P(B)=0.4$ and $P(A\cap\bar{B})=0.5$, where $\bar{B}$ denotes the complement of $B$, then $P\left(B\mid(A\cup\bar{B})\right)$ is equal to
Probability
Solution
$P(A\cap B)=P(A)-P(A\cap\bar B)=0.7-0.5=0.2$. $P(A\cup\bar B)=1-P(\bar A\cap B)=1-(0.4-0.2)=0.8$. $B\cap(A\cup\bar B)=A\cap B$, so $P=\frac{0.2}{0.8}=\frac14$. Option B.