If $P(A) = \frac{7}{13}$, $P(B) = \frac{9}{13}$ and $P(A \cap B) = \frac{4}{13}$, evaluate $P(A|B)$.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{4}{9}$ ##
Given the values:
- $P(A) = \frac{7}{13}$
- $P(B) = \frac{9}{13}$
- $P(A \cap B) = \frac{4}{13}$
Substitute the known values into the formula:
We have $P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{4}{13}}{\frac{9}{13}} = \frac{4}{9}$