The HYPGEOM.DIST function returns the hypergeometric distribution – the probability of a given number of successes from a given population size.

• This function was introduced in Excel 2010 and so is not available in earlier versions.
• HYPGEOM.DIST replaces the HYPGEOMDIST function included in earlier versions of Excel.

### Syntax

=HYPGEOM.DIST(sample_s,number_sample,population_s,number_pop,cumulative)

#### Arguments

Argument Description
sample_s The number of successes in the sample
number_sample The size of the sample
population_s The number of successes in the population
number_pop The population size
cumulative A logical value that determines the form of the function

 TRUE – returns the cumulative distribution function FALSE – returns the probability density function

#### Examples

A B C D
1 Data Description
2 8 Number of successes in the sample
3 20 Sample size
4 40 Number of successes in the population
5 100 Population size
6
7 Formula Result Notes
8 =HYPGEOM.DIST(A2,A3,A4,A5,TRUE) 0.604187 Cumulative hypergeometric distribution function, for sample and population in cells A2:A5
9 =HYPGEOM.DIST(A2,A3,A4,A5,FALSE) 0.200785 Probability hypergeometric distribution function, for sample and in cells A2:A5

Usage note: Use HYPGEOM.DIST for problems with a finite population, where each observation is either a success or a failure, and where each subset of a given size is chosen with equal likelihood.

#### Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if any of the supplied arguments are not recognized as numeric values
#NUM! Occurs if either:

 • the supplied sample_s is < 0 or > number_sample • the supplied number_sample ≤ 0 or > number_population • the supplied population_s ≤ 0 or > number_population • the supplied number_population ≤ 0

The hypergeometric distribution gives the probability of a specific number of successes from a given number of draws, from a finite population, without replacement.

The equation for the hypergeometric distribution is:

where: