1. **Problem Statement:** We have a standard deck of 52 cards. We need to write each event as a set and compute its probability. 2. **Sample Space:** The sample space $S$ consists of 52 cards: 26 red cards (hearts and diamonds) and 26 black cards (clubs and spades). 3. **Event # - Red and not a face card:** - Face cards are Jacks, Queens, Kings. - Red cards: hearts and diamonds. - Non-face red cards are cards from 2 to 10 and aces in hearts and diamonds. - Number of red cards: 26. - Number of face cards in red: 3 (J, Q, K) × 2 suits = 6. - Number of red non-face cards = 26 - 6 = 20. - Event set: $E_1 = \{\text{red cards} \mid \text{not J, Q, K}\}$. - Probability: $P(E_1) = \frac{20}{52} = \frac{5}{13}$. 4. **Event $\$ - Black and even number:** - Black cards: clubs and spades (26 cards). - Even numbers: 2, 4, 6, 8, 10. - Each number appears twice in black suits. - Number of black even cards = 5 numbers × 2 suits = 10. - Event set: $E_2 = \{\text{black cards with denominations } 2,4,6,8,10\}$. - Probability: $P(E_2) = \frac{10}{52} = \frac{5}{26}$. 5. **Event % - Denomination at least 10 (aces high):** - Denominations at least 10: 10, J, Q, K, A. - Each denomination has 4 cards (one per suit). - Number of such cards = 5 × 4 = 20. - Event set: $E_3 = \{10, J, Q, K, A \text{ of all suits}\}$. - Probability: $P(E_3) = \frac{20}{52} = \frac{5}{13}$. 6. **Event & - Denomination at most 4 (aces high):** - Denominations at most 4: 2, 3, 4 (ace is high, so not included). - Each denomination has 4 cards. - Number of such cards = 3 × 4 = 12. - Event set: $E_4 = \{2, 3, 4 \text{ of all suits}\}$. - Probability: $P(E_4) = \frac{12}{52} = \frac{3}{13}$. **Final answers:** - $P(E_1) = \frac{5}{13}$ - $P(E_2) = \frac{5}{26}$ - $P(E_3) = \frac{5}{13}$ - $P(E_4) = \frac{3}{13}$