Let A and B be independent events such that P(A) =0.6 and P(B ) =0.4.
find `P(A nn B) `

Options

A. `0.24`
B. `0.76`
C. `0.56`
D. none of these

Answer

To find the probability of the intersection of two independent events A and B, we can use the formula:

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

### Step-by-Step Solution:

1. **Identify the probabilities of events A and B**:
- Given: \( P(A) = 0.6 \)
- Given: \( P(B) = 0.4 \)

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

3. **Substitute the values into the formula**:
\[ P(A \cap B) = 0.6 \times 0.4 \]

4. **Perform the multiplication**:
\[ P(A \cap B) = 0.24 \]

5. **Conclusion**:
- The probability of the intersection of events A and B is:
\[ P(A \cap B) = 0.24 \]