If A and B are two events, then what is the probability of occurrence of either A or event B ?

Options

A. `P(A) + P(B)`
B. `P(A uu B)`
C. `P(A nn B)`
D. `P(A)P(B)`

Answer

To find the probability of the occurrence of either event A or event B, we can use the formula for the probability of the union of two events.

### Step-by-Step Solution:

1. **Understanding the Events**:
- Let A and B be two events. We want to find the probability of either A occurring or B occurring.

2. **Using the Union Formula**:
- The probability of the union of two events A and B is given by the formula:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
- Here, \( P(A \cup B) \) is the probability that either event A occurs, event B occurs, or both events occur.

3. **Identifying the Components**:
- \( P(A) \) is the probability of event A occurring.
- \( P(B) \) is the probability of event B occurring.
- \( P(A \cap B) \) is the probability that both events A and B occur simultaneously.

4. **Final Expression**:
- Therefore, the probability of occurrence of either A or B can be expressed as:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

5. **Conclusion**:
- The correct answer to the question is that the probability of occurrence of either A or B is represented by \( P(A \cup B) \).