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( barB)`:

Options

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

Answer

To find the probability of the complement of event B (denoted as P(¬B)), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We know that events A and B are mutually exclusive.
- The probabilities of events A and B are given as:
- P(A) = 2/5
- P(B) = 1/2

2. **Recall the Formula for the Complement of an Event**:
- The probability of the complement of an event B is given by:
\[ P(¬B) = 1 - P(B) \]

3. **Substitute the Value of P(B)**:
- We have P(B) = 1/2. Now, we can substitute this value into the formula:
\[ P(¬B) = 1 - \frac{1}{2} \]

4. **Perform the Calculation**:
- Now, calculate the value:
\[ P(¬B) = 1 - 0.5 = 0.5 \]

5. **Final Result**:
- Therefore, the probability of the complement of B is:
\[ P(¬B) = \frac{1}{2} \]

### Summary:
The probability of the complement of event B, P(¬B), is \(\frac{1}{2}\).