If A and B be two mutually exclusive events in a sample space such that , `P(A) = 2/5 and P(B) = 1/2 ` then
find ` P( A nn barB )`:

Options

A. `1/5`
B. `2/5`
C. `4/15`
D. `3/10`

Answer

To solve the problem, we need to find \( P(A \cap \bar{B}) \), where \( A \) and \( B \) are mutually exclusive events. Given that \( P(A) = \frac{2}{5} \) and \( P(B) = \frac{1}{2} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand Mutually Exclusive Events**:
- Mutually exclusive events are events that cannot occur at the same time. This means that \( P(A \cap B) = 0 \).

2. **Identify the Required Probability**:
- We need to find \( P(A \cap \bar{B}) \). This represents the probability of event \( A \) occurring while event \( B \) does not occur.

3. **Use the Formula for Intersection**:
- The formula for the probability of the intersection of two events is:
\[ P(A \cap \bar{B}) = P(A) - P(A \cap B) \]
- Since \( A \) and \( B \) are mutually exclusive, \( P(A \cap B) = 0 \).

4. **Substitute the Known Values**:
- Substitute \( P(A) \) and \( P(A \cap B) \) into the formula:
\[ P(A \cap \bar{B}) = P(A) - 0 = P(A) \]
- Given \( P(A) = \frac{2}{5} \):
\[ P(A \cap \bar{B}) = \frac{2}{5} \]

5. **Conclusion**:
- Therefore, the probability \( P(A \cap \bar{B}) \) is \( \frac{2}{5} \).

### Final Answer:
\[ P(A \cap \bar{B}) = \frac{2}{5} \]