Let A and B be two events. If P(A) = 0.2, P(B)=0.4, `P(A uu B)=0.6`, then `P(A//B)` is equal to :

Options

A. 0.8
B. 0.5
C. 0.3
D. 0

Answer

To solve the problem, we need to find \( P(A|B) \) given the probabilities of events A and B, as well as the probability of their union.

### Step-by-step Solution:

1. **Given Values**:
- \( P(A) = 0.2 \)
- \( P(B) = 0.4 \)
- \( P(A \cup B) = 0.6 \)

2. **Using the Formula for Union of Two Events**:
The formula for the probability of the union of two events is:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Substituting the known values into the equation:
\[ 0.6 = 0.2 + 0.4 - P(A \cap B) \]

3. **Solving for \( P(A \cap B) \)**:
Combine the probabilities on the right side:
\[ 0.6 = 0.6 - P(A \cap B) \]
Rearranging gives:
\[ P(A \cap B) = 0.6 - 0.6 = 0 \]

4. **Finding \( P(A|B) \)**:
The formula for conditional probability is:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
Substituting the values we found:
\[ P(A|B) = \frac{0}{0.4} = 0 \]

### Final Answer:
\[ P(A|B) = 0 \]