Recall the formula for conditional probability.

The conditional probability of event $B$ given event $A$ is defined as:

To find $P(A \cap B)$, multiply both sides of the equation by $P(A)$:

We are given:
$P(A) = 0.5$
$P(B|A) = 0.4$
Substituting these values:

Or, equivalently:

The expression $P(A \cap B) = 0.5 \times 0.4$ matches option B.