If A and B are independent events such that $P(A|B) =\frac{1}{3}$ and $P(B) =\frac{1}{2}$ then the value of $P(A∩B)$ is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{1}{6}$
Given: $P(A\mid B)=\frac{1}{3}$ and $P(B)=\frac{1}{2}$.
Since $A$ and $B$ are independent:
$P(A\mid B)=P(A)$
$P(A)=\frac{1}{3}$
Now:
$P(A\cap B)=P(A)P(B)$
$=\frac{1}{3}\cdot\frac{1}{2}=\frac{1}{6}$
Final answer: $\frac{1}{6}$