If A and B are mutually exclusive events such that `P(A)=0.45 and P(B) = 0.35, ` then `P(Acap B)=`

Options

A. `63/400`
B. `2/5`
C. 0
D. `63/200`

Answer

To solve the problem, we need to find the probability of the intersection of two mutually exclusive events A and B.

### Step-by-Step Solution:

1. **Understand the Definition of Mutually Exclusive Events**:
- Mutually exclusive events are events that cannot occur at the same time. This means that if one event occurs, the other cannot.

2. **Identify Given Probabilities**:
- We are given:
- \( P(A) = 0.45 \)
- \( P(B) = 0.35 \)

3. **Determine the Probability of the Intersection**:
- For mutually exclusive events A and B, the probability of their intersection, denoted as \( P(A \cap B) \), is defined as:
\[ P(A \cap B) = 0 \]
- This is because there are no outcomes that are common to both events A and B.

4. **Conclusion**:
- Therefore, the probability of the intersection of A and B is:
\[ P(A \cap B) = 0 \]

### Final Answer:
\[ P(A \cap B) = 0 \]