This **hypergeometric calculator** can help you compute individual and cumulative hypergeometric probabilities based on population size, no. of successes in population, sample size and no. of successes in sample.

## How does this hypergeometric calculator work?

The algorithm behind this *hypergeometric calculator* is based on the formulas explained below:

1) Individual probability equation: H(x=x given; N, n, s) = [ _{s}C_{x} ] [ _{N-s}C_{n-x} ] / [ _{N}C_{n} ]

2) H(x<x given; N, n, s) is the cumulative probability obtained as the sum of individual probabilities for all cases from (x=0) to (x given – 1).

3) H(x≤x given; N, n, s) is the cumulative probability obtained as the sum of individual probabilities for all cases from (x=0) to (x given).

4) H(x>x given; N, n, s) = 1 - H(x≤x given; N, n, s)

5) H(x≥x given; N, n, s) = H(x=x given; N, n, s) + H(x>x given; N, n, s)

Where:

N = Population size which should be finite.

n = Sample size that should be big enough to ensure relevancy for the population and the experiment being driven.

s = No. of successes in population.

x = No. of successes in sample.

## What is a hypergeometric experiment?

The hypergeometric experiment **has two particularities**:

■ The randomly selections from the *finite population* take place *without replacement*.

■ Each member of the population can either be considered a *success or failure*.

While a *hypergeometric distribution* represents the probability associated with the occurrence of a specific number of successes in a hypergeometric experiment.