Let A and B be the two events such that ` P(A ) = 1/2 ,P(B ) = 1/3 and P(A nn B ) = 1/4` , find
`P(A/B)`

Answer

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

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

### Step 1: Identify the given probabilities
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 of \( P(A \cap B) \) and \( P(B) \) into the formula:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{1}{4}}{\frac{1}{3}} \]

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

\[ P(A|B) = \frac{1}{4} \times \frac{3}{1} = \frac{3}{4} \]

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

\[ P(A|B) = \frac{3}{4} \]

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