If A and B are two events such that `A sub B` and `P(B)ne0`, then which of the following is correct:

Options

A. `P(A//B)=(P(B))/(P(A))`
B. `P(A//B)ltP(A)`
C. `P(A//B)ge P(A)`
D. None of these

Answer

To solve the problem, we need to analyze the relationship between the two events A and B given that A is a subset of B (A ⊆ B) and that the probability of B, P(B), is not equal to 0.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
Since A is a subset of B (A ⊆ B), every outcome in event A is also in event B. This means that the intersection of A and B is simply A itself. Mathematically, we can express this as:
\[ A \cap B = A \]

2. **Using the Probability Formula**:
The probability of the intersection of two events can be expressed using the formula:
\[ P(A \cap B) = P(A) \]
Since we established that \( A \cap B = A \), we can rewrite this as:
\[ P(A) = P(A \cap B) \]

3. **Applying the Conditional Probability**:
The conditional probability of A given B, denoted as \( P(A|B) \), can be calculated using the formula:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
Substituting \( P(A \cap B) = P(A) \) into this formula gives us:
\[ P(A|B) = \frac{P(A)}{P(B)} \]

4. **Conclusion**:
Since \( P(B) \neq 0 \) (as given in the problem), we can conclude that:
\[ P(A|B) = \frac{P(A)}{P(B)} \]
This indicates that the probability of event A occurring given that event B has occurred is equal to the probability of event A divided by the probability of event B.

### Final Result:
Thus, the correct statement is:
\[ P(A|B) = \frac{P(A)}{P(B)} \]