Events $A$ and $B$ are mutually exclusive with $P(A) = 0.4$ and $P(B) = 0.3$. Find $P(A \cup B)$.

Mutually exclusive events cannot occur together, so $P(A \cap B) = 0$. The general addition rule simplifies: $P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.4 + 0.3 - 0 = 0.7$. Option A ($0.12$) is the product $P(A) \cdot P(B)$, which is the joint probability for *independent* events, not mutually exclusive ones. The distinction matters: mutually exclusive means $P(A \cap B) = 0$; independent means $P(A \cap B) = P(A) \cdot P(B)$. These two assumptions cannot both hold unless one event has zero probability.