If A and B are two independent events with P(A) `=1/3 and P(B) = 1/4` , then P(B/A) is equal to

Options

A. `1/4`
B. `1/3`
C. `3/4`
D. 1

Answer

To solve the problem, we need to find \( P(B|A) \), which is the probability of event B occurring given that event A has occurred. Since A and B are independent events, we can use the properties of independent events to find this probability.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We are given \( P(A) = \frac{1}{3} \) and \( P(B) = \frac{1}{4} \).
- Events A and B are independent.

2. **Use the Formula for Conditional Probability**:
- The formula for conditional probability is:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} \]

3. **Find \( P(A \cap B) \)**:
- Since A and B are independent, we can find \( P(A \cap B) \) using the formula:
\[ P(A \cap B) = P(A) \cdot P(B) \]
- Substitute the values:
\[ P(A \cap B) = \left(\frac{1}{3}\right) \cdot \left(\frac{1}{4}\right) = \frac{1}{12} \]

4. **Substitute Back into the Conditional Probability Formula**:
- Now substitute \( P(A \cap B) \) back into the conditional probability formula:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{1}{12}}{\frac{1}{3}} \]

5. **Simplify the Expression**:
- To simplify \( \frac{\frac{1}{12}}{\frac{1}{3}} \), we multiply by the reciprocal:
\[ P(B|A) = \frac{1}{12} \cdot \frac{3}{1} = \frac{3}{12} = \frac{1}{4} \]

6. **Conclusion**:
- Therefore, the probability \( P(B|A) \) is:
\[ P(B|A) = \frac{1}{4} \]

### Final Answer:
\[ P(B|A) = \frac{1}{4} \]