For mutually exclusive events A and B, the joint probability $P(A\cap B)$ is:

• A. $P\left(A\right)\ast P\left(B\right)$
• B. $0$
• C. $P\left(A\right)+P\left(B\right)$
• D. $P\left(A\right|B)$

Answer: (B)

Verified step by step guidance

1. Recall the definition of mutually exclusive events: two events A and B are mutually exclusive if they cannot occur at the same time. This means the intersection of A and B is an empty set.
2. Express this mathematically as \(P(A \cap B) = 0\) because there is no overlap between events A and B.
3. Understand that the joint probability \(P(A \cap B)\) represents the probability that both events A and B happen simultaneously.
4. Since A and B are mutually exclusive, the probability of both happening together is zero, so \(P(A \cap B) = 0\).
5. Note that this is different from the product \(P(A) \times P(B)\), which applies when events are independent, not mutually exclusive.