If `P(A)=2/5` and `P(B)=1/3` and A and B are independent events, then find `P(AnnB)`.

Explanation

To solve the problem, we need to find the probability of the intersection of two independent events A and B, denoted as P(A ∩ B).

### Step-by-Step Solution:

1. **Identify the given probabilities**:
- P(A) = 2/5
- P(B) = 1/3

2. **Understand the concept of independent events**:
- Two events A and B are independent if the occurrence of one does not affect the occurrence of the other. This means that the probability of both A and B occurring together is the product of their individual probabilities.

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

4. **Substitute the values into the formula**:
- Substitute P(A) and P(B) into the formula:
\[ P(A \cap B) = \left(\frac{2}{5}\right) \times \left(\frac{1}{3}\right) \]

5. **Perform the multiplication**:
- Multiply the fractions:
\[ P(A \cap B) = \frac{2 \times 1}{5 \times 3} = \frac{2}{15} \]

6. **Conclusion**:
- Therefore, the probability of the intersection of A and B is:
\[ P(A \cap B) = \frac{2}{15} \]

### Final Answer:
\[ P(A \cap B) = \frac{2}{15} \]

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