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

Options

A. `0.24`
B. `0.56`
C. `0.36`
D. `0.76`

Answer

To find \( P(A \cap \bar{B}) \), where \( A \) and \( B \) are independent events and \( P(A) = 0.6 \) and \( P(B) = 0.4 \), we can follow these steps:

### Step-by-Step Solution:

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

2. **Find the probability of the complement of event B**:
- The complement of \( B \) is denoted as \( \bar{B} \).
- The probability of the complement of \( B \) is calculated as:
\[ P(\bar{B}) = 1 - P(B) = 1 - 0.4 = 0.6 \]

3. **Use the independence of events**:
- Since \( A \) and \( B \) are independent, \( A \) and \( \bar{B} \) are also independent.
- Therefore, we can use the multiplication rule for independent events:
\[ P(A \cap \bar{B}) = P(A) \times P(\bar{B}) \]

4. **Substitute the values into the formula**:
- Now, substituting the known probabilities:
\[ P(A \cap \bar{B}) = P(A) \times P(\bar{B}) = 0.6 \times 0.6 \]

5. **Calculate the final probability**:
- Performing the multiplication:
\[ P(A \cap \bar{B}) = 0.36 \]

Thus, the final answer is:
\[ P(A \cap \bar{B}) = 0.36 \]