1. **Problem Statement:** Calculate the probabilities related to a standard deck of 52 playing cards. 2. **Given:** - Total cards = 52 - Black cards = Clubs + Spades = 26 - Clubs = 13 - Face cards (Jack, Queen, King) = 12 (4 each in 3 suits) 3. **Formulas and Rules:** - Probability of an event $E$ is $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}}$ - Complement rule: $P(\text{not } E) = 1 - P(E)$ 4. **Calculations:** **a. Probability of black card:** $$P(\text{black}) = \frac{26}{52} = \frac{1}{2}$$ **b. Probability of club:** $$P(\text{club}) = \frac{13}{52} = \frac{1}{4}$$ **Complement probabilities:** **a. Probability of not club:** $$P(\text{not club}) = 1 - P(\text{club}) = 1 - \frac{1}{4} = \frac{3}{4}$$ **b. Probability of not face card:** $$P(\text{face card}) = \frac{12}{52} = \frac{3}{13}$$ $$P(\text{not face card}) = 1 - \frac{3}{13} = \frac{10}{13}$$ **Final answers:** - $P(\text{black}) = \frac{1}{2}$ - $P(\text{club}) = \frac{1}{4}$ - $P(\text{not club}) = \frac{3}{4}$ - $P(\text{not face card}) = \frac{10}{13}$