1. **Problem statement:** Find the probability of selecting various cards from a shuffled 52-card deck. 2. **Formula for probability:** $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 3. **Important rules:** - Total cards = 52 - Suits: diamonds (red), hearts (red), spades (black), clubs (black) - Each suit has 13 cards: 2-10, Jack, Queen, King, Ace - Picture cards = Jack, Queen, King 4. **Calculations:** **a) Probability of selecting a Queen:** - Number of Queens = 4 (one per suit) $$P(\text{Queen}) = \frac{4}{52} = \frac{1}{13}$$ **b) Probability of selecting a red Queen:** - Red suits = diamonds, hearts - Red Queens = 2 $$P(\text{red Queen}) = \frac{2}{52} = \frac{1}{26}$$ **c) Probability of selecting the Jack of Hearts:** - Only 1 Jack of Hearts $$P(\text{Jack of Hearts}) = \frac{1}{52}$$ **d) Probability of selecting a Jack of Hearts or Diamonds:** - Jacks in hearts and diamonds = 2 $$P(\text{Jack of Hearts or Diamonds}) = \frac{2}{52} = \frac{1}{26}$$ **e) Probability of selecting any club:** - Clubs = 13 cards $$P(\text{club}) = \frac{13}{52} = \frac{1}{4}$$ **f) Probability of selecting a six or a seven:** - Sixes = 4, Sevens = 4 - Total = 8 $$P(6 \text{ or } 7) = \frac{8}{52} = \frac{2}{13}$$ **g) Probability of selecting a black six:** - Black suits = spades, clubs - Black sixes = 2 $$P(\text{black six}) = \frac{2}{52} = \frac{1}{26}$$ **h) Probability of selecting a picture card (Jack, Queen, King):** - Picture cards per suit = 3 - Total picture cards = $4 \times 3 = 12$ $$P(\text{picture card}) = \frac{12}{52} = \frac{3}{13}$$ **Final answers:** - a) $\frac{1}{13}$ - b) $\frac{1}{26}$ - c) $\frac{1}{52}$ - d) $\frac{1}{26}$ - e) $\frac{1}{4}$ - f) $\frac{2}{13}$ - g) $\frac{1}{26}$ - h) $\frac{3}{13}$