Card Probability Calculator
Calculate the probability of drawing specific cards from a standard 52-card deck.
About Card Probability Calculator
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
Worked example
With the default values below, Card Probability Calculator returns Probability of 0.29947364. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Favorable Cards in Deckaccepts 1–52
- 4
- Cards Drawnaccepts 1–52
- 5
- Desired Successesminimum 0
- 1
- Deck Sizeaccepts 1–52
- 52
Results
- Probability
- 0.29947364
- Odds (1 in X)
- 1 in 3
Step by step
- 1Values used
- 2Formula applied
- 3Probability= 0.29947364
- 4Odds (1 in X)= 1 in 3
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.