1. **Problem:** Determine how many cards in a 52-card deck fit the description: face cards or black cards. 2. **Definitions and facts:** - Total cards: 52 - Suits: Clubs (black), Spades (black), Hearts (red), Diamonds (red) - Each suit has 13 cards. - Face cards: last three cards of each suit (Jack, Queen, King), so 3 face cards per suit. - Black cards: Clubs + Spades = 26 cards. 3. **Step 1: Count face cards.** Face cards per suit = 3 Total face cards = 3 cards/suit × 4 suits = 12 4. **Step 2: Count black cards.** Black cards = Clubs + Spades = 13 + 13 = 26 5. **Step 3: Count face cards that are black.** Face cards in black suits = 3 face cards/suit × 2 black suits = 6 6. **Step 4: Use the formula for union of two sets:** $$|A \cup B| = |A| + |B| - |A \cap B|$$ where - $A$ = face cards - $B$ = black cards 7. **Step 5: Calculate:** $$|\text{face or black}| = 12 + 26 - 6 = 32$$ **Answer:** There are 32 cards that are face cards or black cards in a standard deck.