If E and F are independent events, `P(E)=(1)/(2)` and `P(F)=(1)/(3)`, then `P(E nn F)` is :

Options

A. `(1)/(2)`
B. `(1)/(3)`
C. 0
D. `(1)/(6)`

Answer

To solve the problem, we need to find the probability of the intersection of two independent events E and F, given their individual probabilities.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We are given that:
- \( P(E) = \frac{1}{2} \)
- \( P(F) = \frac{1}{3} \)
- Events E and F are independent.

2. **Use the Formula for Independent Events**:
- For two independent events E and F, the probability of their intersection is given by:
\[ P(E \cap F) = P(E) \times P(F) \]

3. **Substitute the Given Values**:
- Now substitute the values of \( P(E) \) and \( P(F) \) into the formula:
\[ P(E \cap F) = P(E) \times P(F) = \frac{1}{2} \times \frac{1}{3} \]

4. **Calculate the Probability**:
- Perform the multiplication:
\[ P(E \cap F) = \frac{1 \times 1}{2 \times 3} = \frac{1}{6} \]

5. **Conclusion**:
- Therefore, the probability of the intersection of events E and F is:
\[ P(E \cap F) = \frac{1}{6} \]

### Final Answer:
\[ P(E \cap F) = \frac{1}{6} \]