Card Probability Calculator
Find the probability of drawing matching cards without replacement from a stated deck composition.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Deck | integer>=1 |
| Success cards | integer0..deck |
| Draws | integer0..deck |
| Successes | valid hypergeometric support |
Understanding your result
These outputs describe the probability model and event definitions you entered. A probability is a number from 0 to 1; a probability density is not itself the probability of one exact continuous value.
Common mistakes
- Entering 25 instead of 0.25 for a probability, or assuming events are independent when the model requires that assumption.
- Confusing an exact-count probability with a cumulative probability, or replacement with sampling without replacement.
Check your calculation
- Check a zero/certain-event boundary and the stated support of the distribution against the worked example.
Calculation checks, sources and review limits
What is the probability of this many matching cards in a draw without replacement?
Find the probability of drawing matching cards without replacement from a stated deck composition.
Common uses
- Find the probability of drawing matching cards without replacement from a stated deck composition.
How it works
Hypergeometric sample from supplied deck category: C(successCards,k)*C(deck-successCards,draws-k)/C(deck,draws). Trials/draws/counts are limited to 10,000; negative-binomial r and k may each be at most 10,000. Log-factorial arithmetic avoids forming large factorials. Extremely small probabilities can underflow to zero; outputs are numerical estimates, not guarantees about real events.
Worked example
Enter Deck: 52; Success cards: 4; Draws: 1; Successes: 1. The result is Probability: 0.07692307692307693.
FAQ
What is the probability of this many matching cards in a draw without replacement?
Hypergeometric sample from supplied deck category: C(successCards,k)*C(deck-successCards,draws-k)/C(deck,draws). Trials/draws/counts are limited to 10,000; negative-binomial r and k may each be at most 10,000. Log-factorial arithmetic avoids forming large factorials. Extremely small probabilities can underflow to zero; outputs are numerical estimates, not guarantees about real events.
What assumptions and limits apply?
Without replacement, one designated category; no implicit joker or poker-hand assumptions.