If A and B are mutually exclusive, then the P(A and B) is equal to       A.0B.1

Break Down the Problem

1. Understand the Concept of Mutually Exclusive Events: Mutually exclusive events are those that cannot happen at the same time. If event A occurs, event B cannot occur and vice versa.

2. Identify the Probability of Intersection: For two mutually exclusive events A and B, the probability that both A and B occur at the same time is denoted as $P(A \text{ and } B)$.

Relevant Concepts

1. Definition: The probability of two mutually exclusive events occurring simultaneously is defined as: $P(A \text{ and } B) = 0$

Analysis and Detail

1. Explanation: Since A and B cannot happen at the same time, the intersection $P(A \text{ and } B)$ is equal to $0$.

Verify and Summarize

1. Verification: Because mutually exclusive events do not overlap, it confirms that $P(A \text{ and } B)$ is indeed $0$.

Final Answer

The probability $P(A \text{ and } B)$ is equal to 0.