If A and B are mutually exclusive events, then `P(A cap B)` equals

Options

A. 0
B. `1/2`
C. 1
D. `1/4`

Answer

To solve the question regarding the probability of the intersection of two mutually exclusive events A and B, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Mutually Exclusive Events**:
- By definition, two events A and B are said to be mutually exclusive if they cannot occur at the same time. This means that if one event occurs, the other cannot.

2. **Identifying the Intersection**:
- The intersection of two events A and B, denoted as \( P(A \cap B) \), represents the probability that both events occur simultaneously.

3. **Applying the Definition**:
- Since A and B are mutually exclusive, the occurrence of A means that B cannot occur, and vice versa. Therefore, the probability of both A and B occurring at the same time is zero.

4. **Conclusion**:
- Thus, we can conclude that \( P(A \cap B) = 0 \).

### Final Answer:
- Therefore, \( P(A \cap B) = 0 \).

---