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Hypergeometric Probability Calculator

Find the chance of exactly k marked items when sampling without replacement.

Data stays on this deviceConvention explained below
Probability workspace
Probability workspace

Probabilities range from 0 to 1. Check whether the method gives cumulative or exact-count probability.

See the method

Set model parameters

Runs on your device

Your probability

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter population size, marked population items, sample size, marked items drawn.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

P(X=k)=C(K,k)C(N−K,n−k)/C(N,n). Log-gamma evaluates combinations without factorial overflow.

A WORKED EXAMPLE

Using population size = 20, marked population items = 7, sample size = 5, marked items drawn = 2, the result is 0.387383901. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Simple random sampling without replacement. Main result is exact-count probability; impossible marked counts have probability zero. Tiny tails can underflow to zero.

What to keep in mind

Simple random sampling without replacement. Main result is exact-count probability; impossible marked counts have probability zero. Tiny tails can underflow to zero. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Common questions

How do I use this hypergeometric probability calculator?

Find the chance of exactly k marked items when sampling without replacement. Enter population size, marked population items, sample size, marked items drawn. The starting example is editable; use values for the same system or project.

Which assumptions affect this result?

Simple random sampling without replacement. Main result is exact-count probability; impossible marked counts have probability zero. Tiny tails can underflow to zero.

Methodology maintained by ClarityKit. How these tools are built and checked.