Hypergeometric Probability
Calculate sampling success counts without replacement.
Your numbers
Exactly k successes
Use consistent units. The result follows the assumptions you enter.
Scenario comparison
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Formula
P(X=k)=C(K,k)C(N−K,n−k)/C(N,n)
Calculate sampling success counts without replacement.
Worked example
- Population size N
- 20
- Successes in population K
- 7
- Draws n
- 5
- Drawn successes k
- 2
- Exactly k successes
- 38.7383900929 %
- Expected successes
- 1.75
Scope and limitations
Use consistent units. The result follows the assumptions you enter.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: 0dd760853b04 · Example checked: