Card Probability Calculator
Calculate the probability of drawing specific cards from a standard 52-card deck.
Inputs
e.g. 4 aces, 13 hearts
Probability
0.29947364
Odds (1 in X)
1 in 3
Step by step
Values used
Favorable Cards in Deck = 4; Cards Drawn = 5; Desired Successes = 1; Deck Size = 52
Formula applied
P = C(K,k) × C(N−K, n−k) / C(N, n)
Probability
= 0.29947364
Odds (1 in X)
= 1 in 3
How it works
Card probability without replacement follows the hypergeometric distribution. The probability of drawing exactly k favorable cards when drawing n cards from a deck of N cards containing K favorable cards is computed using combinations.
Formula
P = C(K,k) × C(N−K, n−k) / C(N, n)
- N
- Deck size
- K
- Favorable cards in deck
- n
- Cards drawn
- k
- Desired successes
Frequently Asked Questions
What is the probability of drawing at least one ace in 5 cards?
1 − P(no aces) = 1 − C(48,5)/C(52,5) ≈ 0.3412 or 34.1%.
Why is this different from the binomial?
Because cards are drawn without replacement, the trials are not independent. The hypergeometric distribution accounts for the changing deck composition.