Hypergeometric Probability Calculator
Use the hypergeometric model when items are drawn from a finite population without replacement and each item is classified as a success or not.
How to use this calculator
- Enter population size, success items in the population, draw size and exact successes in the draw.
- Check that every input uses the stated units and covers the same period, population or project scope.
- Change one assumption at a time when comparing scenarios.
Formula used by hypergeometric probability calculator
P(X=k) = C(K,k) × C(N−K,n−k) ÷ C(N,n)
- P(X=k) = C(K,k) × C(N−K,n−k) ÷ C(N,n)
- It assumes a simple random sample without replacement and consistent population counts.
- Inputs are validated against the tool-specific constraints; displayed results are rounded for readability.
Worked examples
Worked example
A batch has 50 items, 12 marked items, and a sample of 8; calculate the chance exactly 2 marked items are selected.
The calculator evaluates the combinations in the hypergeometric probability formula.
The calculator evaluates the combinations in the hypergeometric probability formula.
Understanding the result
Use the hypergeometric model when items are drawn from a finite population without replacement and each item is classified as a success or not.
It assumes a simple random sample without replacement and consistent population counts.
Important notes
It assumes a simple random sample without replacement and consistent population counts.
Treat the result as an estimate for the assumptions entered; verify important specifications against the relevant source or professional guidance.
Frequently asked questions
When should I use a hypergeometric model?
Use it when sampling from a finite population without replacement, such as a quality sample from a fixed batch.
How is it different from a binomial model?
The hypergeometric model changes the remaining population after each draw; a binomial model assumes a constant success chance across independent trials.
How should I use this result?
Enter population size, success items in the population, draw size and exact successes in the draw.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Probability — Learn basic probability formulas, complementary probability, and how to calculate simple event chances.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.