A and B are two mutually exclusive events , for which `P(A) = 0.3 , P(B) = p` and `P(A uu B) = 0 .5` . Find the value of `p`.

Answer

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

### Step-by-step Solution:

1. **Understand the Given Information**:
- We know that \( P(A) = 0.3 \)
- We know that \( P(B) = p \)
- We know that \( P(A \cup B) = 0.5 \)
- Since \( A \) and \( B \) are mutually exclusive, \( P(A \cap B) = 0 \).

2. **Use 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 \( P(A \cap B) = 0 \) (because they are mutually exclusive), the formula simplifies to:
\[ P(A \cup B) = P(A) + P(B) \]

3. **Substitute the Known Values**:
- Substitute the known values into the simplified formula:
\[ 0.5 = 0.3 + p \]

4. **Solve for \( p \)**:
- Rearranging the equation gives:
\[ p = 0.5 - 0.3 \]
- Performing the subtraction:
\[ p = 0.2 \]

5. **Conclusion**:
- The value of \( p \) is \( 0.2 \).

### Final Answer:
\[ p = 0.2 \]