If P(A)= 7/13 ,P(B) =9/13 and `P(A cap B) =4/13 ` then P(A/B) is equal to

Options

A. `6/13`
B. `5/13`
C. `4/9`
D. `5/9`

Answer

To find \( P(A|B) \), which is the probability of event A occurring given that event B has occurred, we can use the formula for conditional probability:

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

### Step-by-Step Solution:

1. **Identify the given probabilities:**
- \( P(A) = \frac{7}{13} \)
- \( P(B) = \frac{9}{13} \)
- \( P(A \cap B) = \frac{4}{13} \)

2. **Substitute the values into the conditional probability formula:**
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{4}{13}}{\frac{9}{13}} \]

3. **Simplify the expression:**
- When dividing fractions, we multiply by the reciprocal of the denominator:
\[ P(A|B) = \frac{4}{13} \times \frac{13}{9} \]

4. **Cancel out the common terms:**
- The \( 13 \) in the numerator and denominator cancels out:
\[ P(A|B) = \frac{4}{9} \]

5. **Conclusion:**
- Therefore, the probability \( P(A|B) \) is:
\[ P(A|B) = \frac{4}{9} \]

### Final Answer:
\[ P(A|B) = \frac{4}{9} \]