If A and B are events such that `P(A//B)=P(B//A)`, then :

Options

A. `A sub B` but `A neB`
B. A = B
C. `A nn B = phi`
D. `P(A)=P(B)`

Answer

To solve the problem, we need to analyze the condition given: \( P(A|B) = P(B|A) \).

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The conditional probability \( P(A|B) \) is defined as:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
- Similarly, the conditional probability \( P(B|A) \) is defined as:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} \]

2. **Set Up the Equation**:
- Given \( P(A|B) = P(B|A) \), we can substitute the definitions:
\[ \frac{P(A \cap B)}{P(B)} = \frac{P(A \cap B)}{P(A)} \]

3. **Cross Multiply**:
- Cross multiplying gives us:
\[ P(A \cap B) \cdot P(A) = P(A \cap B) \cdot P(B) \]

4. **Assume \( P(A \cap B) \neq 0 \)**:
- If \( P(A \cap B) \neq 0 \), we can divide both sides by \( P(A \cap B) \):
\[ P(A) = P(B) \]

5. **Conclusion**:
- Therefore, if \( P(A|B) = P(B|A) \), it implies that:
\[ P(A) = P(B) \]

### Final Result:
The relationship that holds true is:
\[ P(A) = P(B) \]