Question

(d) If \( P(A) = \frac{3}{13} \), \( P(B) = \frac{5}{13} \), and \( P(A \cap B) = \frac{2}{13} \), find the value of \( P(B | A) \):

Hint:

Conditional probability is calculated as \( P(B/A) = \frac{P(A \cap B)}{P(A)} \).

Answer 1

The conditional probability is given by: \[ P(B/A) = \frac{P(A \cap B)}{P(A)}. \] Substituting the given values: \[ P(B/A) = \frac{\frac{2}{13}}{\frac{3}{13}} = \frac{2}{3}. \]