If A and B are two events euch that `P(A) != 0 and P(B//A)=1` then

Options

A. `A sub B`
B. `B sub A`
C. `B = phi`
D. none of these

Answer

To solve the problem, we need to analyze the given conditions about the events A and B.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We are given that \( P(A) \neq 0 \) and \( P(B|A) = 1 \). The notation \( P(B|A) \) represents the conditional probability of event B given that event A has occurred.

2. **Using the Formula for Conditional Probability**:
The formula for conditional probability is:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} \]
Since we know that \( P(B|A) = 1 \), we can substitute this into the formula:
\[ 1 = \frac{P(A \cap B)}{P(A)} \]

3. **Rearranging the Equation**:
From the equation above, we can multiply both sides by \( P(A) \):
\[ P(A \cap B) = P(A) \]

4. **Interpreting the Result**:
The equation \( P(A \cap B) = P(A) \) means that the probability of both A and B occurring is equal to the probability of A occurring. This implies that whenever A occurs, B must also occur. Therefore, A is a subset of B.

5. **Conclusion**:
Since \( A \) is a subset of \( B \), we can conclude:
\[ A \subseteq B \]

### Final Answer:
Thus, the final conclusion is that event A is a subset of event B.

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