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( barA)`:

Options

A. `2/5`
B. `3/5`
C. `4/5`
D. `6/7`

Answer

To find \( P(\bar{A}) \), which is the probability of the complement of event A, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Complement**:
The complement of an event A, denoted as \( \bar{A} \), represents all outcomes in the sample space that are not in A. The probability of the complement can be calculated using the formula:
\[ P(\bar{A}) = 1 - P(A) \]

2. **Identify Given Probabilities**:
From the problem, we know:
\[ P(A) = \frac{2}{5} \]

3. **Substitute the Probability of A into the Formula**:
Now, we can substitute the value of \( P(A) \) into the complement formula:
\[ P(\bar{A}) = 1 - P(A) = 1 - \frac{2}{5} \]

4. **Calculate the Value**:
To perform the subtraction, we need to express 1 as a fraction with a denominator of 5:
\[ 1 = \frac{5}{5} \]
Therefore,
\[ P(\bar{A}) = \frac{5}{5} - \frac{2}{5} = \frac{3}{5} \]

5. **Final Result**:
Thus, the probability of the complement of event A is:
\[ P(\bar{A}) = \frac{3}{5} \]

### Summary:
The final answer is:
\[ P(\bar{A}) = \frac{3}{5} \]