# How to use HYPGEOM.DIST Function in Excel

The HYPGEOM.DIST function returns the hypergeometric distribution. HYPGEOM.DIST returns the probability of a given number of sample successes, given the sample size, population successes, and population size.

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.

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

The HYPGEOM.DIST function syntax has the following arguments:

• Sample_s     Required. The number of successes in the sample.
• Number_sample     Required. The size of the sample.
• Population_s     Required. The number of successes in the population.
• Number_pop     Required. The population size.
• Cumulative     Required. A logical value that determines the form of the function. If cumulative is TRUE, then HYPGEOM.DIST returns the cumulative distribution function; if FALSE, it returns the probability mass function.

Example: Let’s look at some Excel HYPGEOM.DIST function examples and explore how to use the HYPGEOM.DIST function as a worksheet function in Microsoft Excel:

Syntax:  =HYPGEOM.DIST(B1,B2,B3,B4,TRUE)

Result: 0.903252442

Based on the Excel spreadsheet above, the following HYPGEOM.DIST examples would return:

Syntax: =HYPGEOM.DIST(B1,B2,B3,B4,TRUE)
Result: 0.903252442

Syntax: =HYPGEOM.DIST(B1,B2,B3,B4,FALSE)
Result: 0.246776524

Note:

• All arguments are truncated to integers.
• If any argument is nonnumeric, HYPGEOM.DIST returns the #VALUE! error value.
• If sample_s < 0 or sample_s is greater than the lesser of number_sample or population_s, HYPGEOM.DIST returns the #NUM! error value.
• If sample_s is less than the larger of 0 or (number_sample – number_population + population_s), HYPGEOM.DIST returns the #NUM! error value.
• If number_sample ≤ 0 or number_sample > number_population, HYPGEOM.DIST returns the #NUM! error value.
• If population_s ≤ 0 or population_s > number_population, HYPGEOM.DIST returns the #NUM! error value.
• If number_pop ≤ 0, HYPGEOM.DIST returns the #NUM! error value.
• The equation for the hypergeometric distribution is:

where:

x = sample_s

n = number_sample

M = population_s

N = number_pop

HYPGEOM.DIST is used in sampling without replacement from a finite population.