If `A` and `B` are two events such that `A nn B !> phi, p(A/B) = P(B/A)`. Then,

Options

A. `AsubB` but `A!=B`
B. `A=B`
C. `AnnB=phi`
D. `P(A)=P(B)`

Explanation

To solve the problem step by step, we start with the given conditions and manipulate them using the properties of probability.

### Step-by-Step Solution:

1. **Given Information**:
We are given that:
- \( A \cap B \neq \phi \) (the intersection of events A and B is not empty)
- \( P(A/B) = P(B/A) \)

2. **Using the Definition of Conditional Probability**:
The conditional probability \( P(A/B) \) can be expressed as:
\[ P(A/B) = \frac{P(A \cap B)}{P(B)} \]
Similarly, \( P(B/A) \) can be expressed as:
\[ P(B/A) = \frac{P(A \cap B)}{P(A)} \]

3. **Setting the Two Expressions Equal**:
Since \( P(A/B) = P(B/A) \), we can set the two expressions equal to each other:
\[ \frac{P(A \cap B)}{P(B)} = \frac{P(A \cap B)}{P(A)} \]

4. **Cross Multiplying**:
Cross multiplying gives us:
\[ P(A \cap B) \cdot P(A) = P(A \cap B) \cdot P(B) \]

5. **Assuming \( P(A \cap B) \neq 0 \)**:
Since \( A \cap B \neq \phi \), we know \( P(A \cap B) > 0 \). Thus, we can divide both sides by \( P(A \cap B) \):
\[ P(A) = P(B) \]

6. **Conclusion**:
We have established that \( P(A) = P(B) \). This means that the probabilities of events A and B are equal.

7. **Interpreting the Result**:
If the probabilities of A and B are equal, and since they are events, we can infer that the number of favorable outcomes for A is equal to the number of favorable outcomes for B, given that they are defined over the same sample space.

### Final Result:
From the above steps, we conclude that:
- \( P(A) = P(B) \)
- The number of elements in A is equal to the number of elements in B, which implies that \( A \) and \( B \) are equivalent in terms of their outcomes.