If ` P(A) = (1)/(2), P(B) = (1)/(3) and P(A nn B) = (1)/(4)` then P(B/A)

Options

A. `(1)/(2)`
B. 0
C. `(1)/(2)`
D. `(1)/(3)`

Answer

To find \( P(B|A) \), we can use the formula for conditional probability:

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

### Step 1: Identify the given values
From the question, we have:
- \( P(A) = \frac{1}{2} \)
- \( P(B) = \frac{1}{3} \)
- \( P(A \cap B) = \frac{1}{4} \)

### Step 2: Substitute the values into the formula
Now, we can substitute the values into the conditional probability formula:

\[ P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{1}{4}}{\frac{1}{2}} \]

### Step 3: Simplify the fraction
To simplify \( \frac{\frac{1}{4}}{\frac{1}{2}} \), we multiply by the reciprocal of the denominator:

\[ P(B|A) = \frac{1}{4} \times \frac{2}{1} = \frac{2}{4} = \frac{1}{2} \]

### Final Answer
Thus, the probability \( P(B|A) \) is:

\[ P(B|A) = \frac{1}{2} \]

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