The happening of any one of the two mutually exclusive events A and B is

Options

A. `P[A].P[B]`
B. `P(A)+P(B)-P(A capB)`
C. `P[A]+P[B]`
D. none

Answer

To solve the problem regarding the probability of the happening of either event A or event B, which are mutually exclusive events, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding 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. **Identifying the Required Probability**:
- We need to find the probability of either event A or event B occurring. This is represented as P(A ∪ B), which denotes the probability of the union of events A and B.

3. **Using the Formula for Probability of Union**:
- The general formula for the probability of the union of two events A and B is:
\[ P(A ∪ B) = P(A) + P(B) - P(A ∩ B) \]
- Here, P(A ∩ B) represents the probability that both events A and B occur simultaneously.

4. **Applying the Condition of Mutual Exclusivity**:
- Since events A and B are mutually exclusive, the probability of both events occurring together, P(A ∩ B), is 0. This simplifies our formula:
\[ P(A ∪ B) = P(A) + P(B) - 0 \]
- Therefore, we can simplify it to:
\[ P(A ∪ B) = P(A) + P(B) \]

5. **Conclusion**:
- The probability of either event A or event B occurring is simply the sum of their individual probabilities:
\[ P(A ∪ B) = P(A) + P(B) \]

### Final Answer:
Thus, the probability of the happening of any one of the two mutually exclusive events A and B is:
\[ P(A ∪ B) = P(A) + P(B) \]