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

Options

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

Answer

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

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

Where:
- \( P(A|B) \) is the probability of event A occurring given that event B has occurred.
- \( P(A \cap B) \) is the probability of both events A and B occurring.
- \( P(B) \) is the probability of event B occurring.

Given:
- \( P(A) = \frac{1}{2} \)
- \( P(B) = 0 \)

Now, we can substitute these values into the formula.

### Step 1: Identify the values
We have:
- \( P(A) = \frac{1}{2} \)
- \( P(B) = 0 \)

### Step 2: Calculate \( P(A|B) \)
Using the formula for conditional probability:

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

Since \( P(B) = 0 \), we can see that the denominator of our fraction is zero.

### Step 3: Determine the result
Since division by zero is undefined in mathematics, we conclude that:

\[ P(A|B) \text{ is not defined} \]

### Final Answer:
Thus, the answer is that \( P(A|B) \) is **not defined**.

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