If A and B are mutually exclusive, then the P(A and B) is equal toa. 0b. 1c. 0.5d. 0.75

Break Down the Problem

1. Understanding Mutually Exclusive Events: Events A and B are mutually exclusive, meaning they cannot occur at the same time.
2. Event Probability: The probability of both events occurring simultaneously (denoted as P(A and B)) in mutually exclusive events.

Relevant Concepts

1. Definition of Mutually Exclusive: If A and B are mutually exclusive, then: $P(A \text{ and } B) = 0$ This is because, by definition, if one event occurs, the other cannot.

Analysis and Detail

1. Calculating P(A and B):
   • There is no situation in a mutually exclusive scenario where both events A and B can happen together, hence the calculation directly leads us to: $P(A \text{ and } B) = 0$

Verify and Summarize

1. Verification: Since mutually exclusive events cannot occur together, P(A and B) is confirmed as 0.
2. Summary: For mutually exclusive events A and B, the probability of both occurring simultaneously is always zero.

Final Answer

The correct answer is a. 0.