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

$\frac{1}{6}$

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: $\frac{1}{6}$