If the events A and B are independent, then `P(AcapB)` is equal to

Options

A. P(A)+P(B)
B. P(A)-P(B)
C. P(A)`cdotP(B)`
D. P(A)/P(B)

Explanation

To solve the problem, we need to understand the concept of independent events in probability.

### Step-by-Step Solution:

1. **Understanding Independent Events**:
- Two events A and B are said to be independent if the occurrence of one does not affect the occurrence of the other.

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

3. **Formula for Independent Events**:
- For independent events, the probability of the intersection of A and B is given by the formula:
\[ P(A \cap B) = P(A) \times P(B) \]

4. **Identifying the Correct Option**:
- From the options provided:
- Option 1: \( P(A) + P(B) \) (Incorrect)
- Option 2: \( P(A) - P(B) \) (Incorrect)
- Option 3: \( P(A) \times P(B) \) (Correct)
- Option 4: \( \frac{P(A)}{P(B)} \) (Incorrect)

5. **Conclusion**:
- Therefore, the correct answer is:
\[ P(A \cap B) = P(A) \times P(B) \]

### Final Answer:
The probability \( P(A \cap B) \) is equal to \( P(A) \times P(B) \).

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