Step 1: Recall the formula for conditional probability. The conditional probability of event $B$ given event $A$ is defined as: $$P(B|A) = \frac{P(A \cap B)}{P(A)}$$ Step 2: Rearrange the formula to solve for $P(A \cap B)$. To find $P(A \cap B)$, multiply both sides of the equation by $P(A)$: $$P(A \cap B) = P(B|A) \times P(A)$$ Step 3: Substitute the given values into the formula. We are given: $P(A) = 0.5$ $P(B|A) = 0.4$ Substituting these values: $$P(A \cap B) = 0.4 \times 0.5$$ Or, equivalently: $$P(A \cap B) = 0.5 \times 0.4$$ Step 4: Compare the derived expression with the given options. The expression $P(A \cap B) = 0.5 \times 0.4$ matches option B. The final answer is $\boxed{\text{B}}$ Last free one today — make it count tomorrow, or type /upgrade for unlimited.