Probability

Concept:For independent events $A$ and $B$, $P(A \cap B) = P(A)P(B)$. For mutually exclusive events, $P(A \cap B) = 0$.Explanation:If $A$ and $B$ are independent and mutually exclusive, then $P(A)P(B) = 0$, implying either $P(A)=0$ or $P(B)=0$. Unless one event has zero probability, independent events cannot be mutually exclusive. Thus, they cannot be mutually exclusive (assuming non‑zero probabilities). Independence does not prevent events from being exhaustive, so option (c) is false. Therefore, only option (b) is correct.Answer:Option B.