If `P(A)=(3)/(5)` and `P(B)=(1)/(5)`, then the value of `P(A nn B)` when A and B are independent events is :

Options

A. `(3)/(25)`
B. `(3)/(28)`
C. `(2)/(7)`
D. `(2)/(11)`

Answer

To find the value of \( P(A \cap B) \) when events A and B are independent, we can use the formula for the intersection of two independent events:

\[ P(A \cap B) = P(A) \times P(B) \]

### Step-by-Step Solution:

1. **Identify the probabilities of events A and B:**
- Given \( P(A) = \frac{3}{5} \)
- Given \( P(B) = \frac{1}{5} \)

2. **Use the formula for independent events:**
- Since A and B are independent, we can apply the formula:
\[ P(A \cap B) = P(A) \times P(B) \]

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

4. **Perform the multiplication:**
- Multiply the fractions:
\[ P(A \cap B) = \frac{3 \times 1}{5 \times 5} = \frac{3}{25} \]

5. **Final answer:**
- Therefore, the value of \( P(A \cap B) \) is:
\[ P(A \cap B) = \frac{3}{25} \]