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Calculators/Statistics/Hypergeometric probability
Statistics

Hypergeometric probability calculator

Chance of drawing an exact number of successes from a finite population, without replacement.

What this calculator does

Hypergeometric probability works out chance of drawing an exact number of successes from a finite population, without replacement. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.

The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.

The formula

FormulaP(X=k) = C(K,k)·C(N−K,n−k) / C(N,n)

The inputs explained

FieldWhat to enter
Population size (N)A number. Starts at 50.
Successes in population (K)A number. Starts at 10.
Sample size (n)A number. Starts at 8.
Successes wanted in sample (k)A number. Starts at 3.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

How the answer changes with population size (n)

Every other input is held at the calculator’s starting values while population size (n) varies. Select any row to load that scenario into the calculator.

How the answer changes with population size (n)
Population size (N)P(exactly k successes)Expected successes (mean)Standard deviation
2533.3%3.201.17
37.524.1%2.111.12
5014.7%1.601.05
755.88%1.070.91
1002.83%0.800.82
1500.952%0.530.69