Hypergeometric Calculator
Calculate the probability of a success count when sampling without replacement.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Population size | integer>=1 |
| Successes in population | integer0..N |
| Number of trials | integer0..N |
| Successes / event count | integer0..min(K,n), n-k<=N-K |
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 chance of drawing this many successes without replacement?
Calculate the probability of a success count when sampling without replacement.
Common uses
- Calculate the probability of a success count when sampling without replacement.
How it works
PMF=C(K,k)*C(N-K,n-k)/C(N,n) 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 Population size: 10; Successes in population: 4; Number of trials: 2; Successes / event count: 1. The result is Pmf: 0.5333333333333333.
FAQ
What is the chance of drawing this many successes without replacement?
PMF=C(K,k)*C(N-K,n-k)/C(N,n) 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?
Uniform draws without replacement; stable log-combination implementation.