If A and B are two independent events such that :
`P(A uu B)=0.60` and `P(A)=0.2`, then P(B) = ___________.

Answer

To find \( P(B) \) given that \( P(A \cup B) = 0.60 \) and \( P(A) = 0.2 \), we can use the formula for the probability of the union of two independent events:

### Step-by-Step Solution:

1. **Understand the Formula for Union of Two Events**:
The formula for the probability of the union of two events \( A \) and \( B \) is:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Since \( A \) and \( B \) are independent, we have:
\[ P(A \cap B) = P(A) \cdot P(B) \]

2. **Substitute Known Values**:
Substitute the known values into the union formula:
\[ P(A \cup B) = P(A) + P(B) - P(A) \cdot P(B) \]
Plugging in the values:
\[ 0.60 = 0.2 + P(B) - (0.2 \cdot P(B)) \]

3. **Simplify the Equation**:
Rearrange the equation:
\[ 0.60 = 0.2 + P(B) - 0.2P(B) \]
Combine like terms:
\[ 0.60 = 0.2 + P(B)(1 - 0.2) \]
This simplifies to:
\[ 0.60 = 0.2 + 0.8P(B) \]

4. **Isolate \( P(B) \)**:
Subtract \( 0.2 \) from both sides:
\[ 0.60 - 0.2 = 0.8P(B) \]
\[ 0.40 = 0.8P(B) \]

5. **Solve for \( P(B) \)**:
Divide both sides by \( 0.8 \):
\[ P(B) = \frac{0.40}{0.8} = 0.50 \]

### Final Answer:
\[ P(B) = 0.50 \]