If (A) = 0.8, P(B) = 0.5 and `P(B//A)=0.4`, then `P(A//B)=0.64`.

Answer

To determine whether the statement \( P(A|B) = 0.64 \) is true or false given the probabilities \( P(A) = 0.8 \), \( P(B) = 0.5 \), and \( P(B|A) = 0.4 \), we can use the formula for conditional probability.

### Step-by-step solution:

1. **Use the formula for conditional probability**:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} \]
Rearranging this gives:
\[ P(A \cap B) = P(B|A) \cdot P(A) \]

2. **Substitute the known values**:
\[ P(A \cap B) = 0.4 \cdot 0.8 \]

3. **Calculate \( P(A \cap B) \)**:
\[ P(A \cap B) = 0.32 \]

4. **Now, use the formula for \( P(A|B) \)**:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

5. **Substitute the values we have**:
\[ P(A|B) = \frac{0.32}{0.5} \]

6. **Calculate \( P(A|B) \)**:
\[ P(A|B) = 0.64 \]

7. **Conclusion**:
Since we have calculated \( P(A|B) = 0.64 \), the statement \( P(A|B) = 0.64 \) is true.