If `P(A)=(1)/(2)` and `P(B)=0`, then `P(A//B)` is equal to :

Options

A. 0
B. `(1)/(2)`
C. not defined
D. 1

Answer

To solve the problem, we need to find \( P(A|B) \), which is the conditional probability of event A given event B. The formula for conditional probability is:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

### Step 1: Identify the given probabilities
From the problem, we have:
- \( P(A) = \frac{1}{2} \)
- \( P(B) = 0 \)

### Step 2: Substitute the values into the conditional probability formula
We can substitute the values we have into the conditional probability formula:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{P(A \cap B)}{0} \]

### Step 3: Analyze the denominator
Since \( P(B) = 0 \), the denominator of our fraction becomes zero. In probability theory, division by zero is undefined.

### Conclusion
Thus, \( P(A|B) \) is not defined because we cannot divide by zero.

### Final Answer
\[ P(A|B) \text{ is not defined.} \]

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