Hypergeometric Distribution Calculator
Calculate hypergeometric distribution using your data.
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What this tool does
Calculate hypergeometric distribution using your data. Sampling is without replacement from a finite population — unlike the binomial, each draw changes the remaining composition.
How to use the Hypergeometric Distribution Calculator
- Enter or select population size (n).
- Enter or select successes in population (k).
- Enter or select draws without replacement (n).
- Enter or select successes drawn (k).
- Read the calculated result; change any measurement to compare alternatives.
Formula
P(X=k) = C(K,k)·C(N−K, n−k) / C(N, n)
- NN
- Population size (N)
- KK
- Successes in population (K)
- nn
- Draws without replacement (n)
- kk
- Successes drawn (k)
Sampling is without replacement from a finite population — unlike the binomial, each draw changes the remaining composition.
Worked example
For hypergeometric distribution calculator, the following measurements illustrate the exact method: Population size (N): 50; Successes in population (K): 10; Draws without replacement (n): 5; Successes drawn (k): 2.
Inputs
- Population size (N)50
- Successes in population (K)10
- Draws without replacement (n)5
- Successes drawn (k)2
Result
- P(X = k) (%)20.98
- P(X ≤ k) (%)95.17
- Expected successes drawn1
Results explained
- P(X = k) (%)
- P(X = k) (%) from the formula above. Sampling is without replacement from a finite population — unlike the binomial, each draw changes the remaining composition.
- P(X ≤ k) (%)
- P(X ≤ k) (%) from the formula above. Sampling is without replacement from a finite population — unlike the binomial, each draw changes the remaining composition.
- Expected successes drawn
- Expected successes drawn from the formula above. Sampling is without replacement from a finite population — unlike the binomial, each draw changes the remaining composition.
Frequently asked questions
P(X=k) = C(K,k)·C(N−K, n−k) / C(N, n)
Sampling is without replacement from a finite population — unlike the binomial, each draw changes the remaining composition.
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.