Spades ♠
Hearts ♥
Clubs ♣
Diamonds ♦
Probability Facts for Cards
- Total cards: 52 (4 suits × 13 ranks).
- Probability of drawing a specific card (e.g., Ace of Spades): 1/52 ≈ 0.0192 (1.92%).
- Probability of drawing a specific suit (e.g., Hearts): 13/52 = 1/4 = 0.25 (25%).
- Probability of drawing a face card (J, Q, K): 12/52 = 3/13 ≈ 0.2308 (23.08%).
- Probability of drawing an Ace: 4/52 = 1/13 ≈ 0.0769 (7.69%).
- Probability of drawing a red card (Hearts or Diamonds): 26/52 = 1/2 = 0.5 (50%).
- Probability of drawing a card of a specific rank (e.g., any 7): 4/52 = 1/13 ≈ 0.0769 (7.69%).
- With replacement, probabilities remain constant; without replacement, they change (e.g., after drawing one card, 51 cards remain).
- Permutation Formula: For arranging r cards from n cards (order matters): P(n,r) = n! / (n-r)!
- Combination Formula: For choosing r cards from n cards (order doesn't matter): C(n,r) = n! / (r!(n-r)!)
- Example: Number of ways to choose 5 cards (e.g., for poker hand): C(52,5) = 52! / (5!47!) = 2,598,960.