## Definition The ==Probability Multiplication Rules== give the probability of the intersection of events. For any two events $A$ and $B$: $ P(A \cap B) = P(A) \cdot P(B \mid A) = P(B) \cdot P(A \mid B) $ If $A$ and $B$ are independent, this simplifies to $P(A \cap B) = P(A) \cdot P(B)$. > [!example]- A bag has 5 red and 3 blue marbles. Two marbles are drawn without replacement. What is the probability both are red? > $ P(R_1 \cap R_2) = P(R_1) \cdot P(R_2 \mid R_1) = \frac{5}{8} \cdot \frac{4}{7} = \frac{20}{56} = \frac{5}{14} \approx 0.357 $