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A standard deck has 52 cards: 4 suits (Hearts ♥, Diamonds ♦, Clubs ♣, Spades ♠) × 13 ranks (A, 2-10, J, Q, K). That means 4 of each rank (4 Aces, 4 Kings, etc.) and 13 cards in each suit.
What does "NOT a Heart" mean?
A deck has 4 suits. "NOT a Heart" means drawing from any of the other 3 suits: Diamonds ♦, Clubs ♣, or Spades ♠.
Why use complement?
We could add up 13 + 13 + 13 = 39 cards from the three other suits... Or simply find P(Heart) = 13/52 and subtract from 1. Much simpler!
A standard deck is divided equally into 4 suits. Each suit has exactly 13 cards (A, 2-10, J, Q, K):
Hearts
13 cards
(what we avoid)
Diamonds
13 cards ✓
Clubs
13 cards ✓
Spades
13 cards ✓
NOT Heart = 13 + 13 + 13 = 39 cards (the green suits)
Draw one card from a standard deck. What's the probability it's NOT a Heart?
Find P(Heart) — the event we DON'T want
13 Hearts out of 52 total cards:
Apply the complement rule
"NOT Heart" = 1 - P(Heart). This gives us Diamonds + Clubs + Spades:
Result:
✓ 3 out of 4 suits means 75% of the deck is NOT Hearts ✓
Verification:
| Event | Count | P(E) | P(NOT E) |
|---|---|---|---|
| Any suit (♥/♦/♣/♠) | 13 | ||
| Red (♥ or ♦) | 26 | ||
| Black (♣ or ♠) | 26 |