If A and B are mutually exclusive events such that `P(A) =0.4 ,P(B) =x` and
`P(A uu B) =0.5 " then " x=?`

Options

A. 0.2
B. 0.1
C. `(4)/(5)`
D. none of these

Explanation

To solve the problem, we need to find the value of \( x \) given the probabilities of two mutually exclusive events \( A \) and \( B \).

### Step-by-Step Solution:

1. **Understanding Mutually Exclusive Events**:
- Mutually exclusive events are events that cannot occur at the same time. This means that the probability of both events happening together is zero:
\[ P(A \cap B) = 0 \]

2. **Given Probabilities**:
- We are given:
- \( P(A) = 0.4 \)
- \( P(B) = x \)
- \( P(A \cup B) = 0.5 \)

3. **Using the Formula for Union of Two Events**:
- The formula for the probability of the union of two events is:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
- Since \( A \) and \( B \) are mutually exclusive, we can substitute \( P(A \cap B) = 0 \):
\[ P(A \cup B) = P(A) + P(B) \]

4. **Substituting the Known Values**:
- Now, substituting the known values into the equation:
\[ 0.5 = 0.4 + x \]

5. **Solving for \( x \)**:
- To find \( x \), we rearrange the equation:
\[ x = 0.5 - 0.4 \]
- Therefore:
\[ x = 0.1 \]

6. **Conclusion**:
- The value of \( x \) is \( 0.1 \).

### Final Answer:
\[ x = 0.1 \]