Question

If $A$ and $B$ are two events such that $P(A) = 0.6$, $P(B) = 0.3$ and $P(A \cap B) = 0.15$, find $P(A|B)$.

Hint:

Conditional probability formula: $P(A|B) = \dfrac{P(A \cap B)}{P(B)}$, valid when $P(B) > 0$.

Answer 1

We know the formula for conditional probability: \[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

Step 1: Substitute values. \[ P(A|B) = \frac{0.15}{0.3} \]

Step 2: Simplify. \[ P(A|B) = 0.5 \]

Final Answer: \[ \boxed{0.5} \]