What is Hypergeometric Distribution?

It describes the probability of k successes in n draws, without replacement, from a finite population of size N that contains exactly K objects with that feature.

Difference from Binomial?

Binomial assumes replacement (probability stays constant). Hypergeometric assumes NO replacement (probability changes after each draw).

Drawing 5 cards from a deck and getting exactly 2 Hearts.

Hypergeometric Calculator

Sampling without replacement: Probability of k successes in n draws.

Population Size (N)

Successes in Pop (K)

Sample Size (n)

Observed Successes (k)

Target number of successes

P(X = 2)

0

P(X ≤ 2) = 0

Probability Mass Function

Mean

Variance

Formulas

PMF

Mean

Variance

Frequently Asked Questions

How to Use

About the Hypergeometric

What it calculates

This hypergeometric solves mathematical and statistical problems using standard formulas. Successes in draws w/o replacement.

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Hypergeometric.

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