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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 an Ace" mean?
When you draw a card, "NOT an Ace" means you get any of the other 12 ranks: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, or King.
Why use complement?
We could count all 48 non-Ace cards... but it's easier to count the 4 Aces and subtract from the total. That's the power of the complement rule!
Draw one card from a standard 52-card deck. What's the probability it's NOT an Ace?
The 4 Aces in a standard deck:
One Ace in each suit = 4 Aces total
Find P(Ace) — the event we DON'T want
4 Aces out of 52 cards, so:
Apply the complement rule
"NOT Ace" is the complement of "Ace". Since all probabilities sum to 1:
Result:
✓ Verification: 48 non-Ace cards out of 52 = 48/52 = 12/13 ✓
For any single rank (Ace, King, Queen, etc.):
Drawing that rank
NOT drawing that rank