1. **State the problem:** We need to find the probability that a card drawn from a standard deck of 52 cards is either a black card or a 3. 2. **Recall the formula for probability of union of two events:** $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ where $A$ is the event "card is black" and $B$ is the event "card is a 3". 3. **Calculate each probability:** - Total cards: 52 - Number of black cards (clubs and spades): 26 - Number of 3s: 4 (one in each suit) So, $$P(A) = \frac{26}{52} = \frac{1}{2}$$ $$P(B) = \frac{4}{52} = \frac{1}{13}$$ 4. **Calculate the intersection $P(A \cap B)$:** - Black cards that are 3s: 3 of clubs and 3 of spades, so 2 cards $$P(A \cap B) = \frac{2}{52} = \frac{1}{26}$$ 5. **Apply the formula:** $$P(A \cup B) = \frac{1}{2} + \frac{1}{13} - \frac{1}{26}$$ 6. **Find common denominator and simplify:** Common denominator is 26. $$\frac{1}{2} = \frac{13}{26}, \quad \frac{1}{13} = \frac{2}{26}$$ So, $$P(A \cup B) = \frac{13}{26} + \frac{2}{26} - \frac{1}{26} = \frac{14}{26}$$ 7. **Simplify the fraction:** $$\frac{14}{26} = \frac{\cancel{14}^{7}}{\cancel{26}^{13}} = \frac{7}{13}$$ **Final answer:** $$\boxed{\frac{7}{13}}$$