## Definition The ==Probability Addition Rule== states that for any two events $A$ and $B$: $ P(A \cup B) = P(A) + P(B) - P(A \cap B) $ When $A$ and $B$ are mutually exclusive ($A \cap B = \emptyset$), this simplifies to $P(A \cup B) = P(A) + P(B)$. This rule is a direct application of the inclusion-exclusion principle to two events. > [!example]- A card is drawn from a standard 52-card deck. What is the probability it is a heart or a face card? > Let $H$ = heart (13 cards), $F$ = face card (12 cards). Hearts that are face cards: $|H \cap F| = 3$. > $ P(H \cup F) = \frac{13}{52} + \frac{12}{52} - \frac{3}{52} = \frac{22}{52} = \frac{11}{26} \approx 0.423 $