HYPGEOMDIST Function

All versions (legacy) Compatibility

The Excel HYPGEOMDIST function returns the hypergeometric distribution — the probability of a given number of successes when sampling without replacement. It is a legacy function; Microsoft replaced it in Excel 2010 with HYPGEOM.DIST, which adds a cumulative option.

Quick answer:

=HYPGEOMDIST(1,4,8,20) probability of exactly 1 success ≈ 0.3633

Syntax

=HYPGEOMDIST(sample_s, number_sample, population_s, number_population)

Argument		Description
`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_population`	Required	The size of the population.

How to use it

HYPGEOMDIST models drawing without replacement — for example, the chance of pulling a certain number of defective parts from a finite batch. Unlike the modern function, the legacy form has no cumulative argument: it always returns the probability of exactly sample_s successes.

=HYPGEOMDIST(1,4,8,20) // exactly 1 success ≈ 0.3633

=HYPGEOMDIST(2,4,8,20) // exactly 2 successes ≈ 0.3633

Here we draw a sample of 4 from a population of 20 that contains 8 successes. All four arguments must be non-negative integers, and each count cannot exceed its container (e.g. sample_s ≤ number_sample).

Use HYPGEOM.DIST in Excel 2010 and later. The modern HYPGEOM.DIST adds a fifth cumulative argument so you can get a running total, not just the exact-count probability. HYPGEOMDIST is kept only for backward compatibility.

Try it: interactive demo

Live demo

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example

Result:

Practice workbook

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Frequently asked questions

Should I use HYPGEOMDIST or HYPGEOM.DIST?

Use HYPGEOM.DIST in Excel 2010 or later. It accepts the same four counts plus a cumulative flag; HYPGEOMDIST is retained only so older workbooks keep working.

Why does the legacy HYPGEOMDIST have no cumulative argument?

The original function only computes the probability of exactly sample_s successes. To get a cumulative probability you must sum several calls, or switch to HYPGEOM.DIST and set cumulative to TRUE.

How is the hypergeometric distribution different from the binomial?

The binomial assumes sampling with replacement (constant probability), while the hypergeometric samples without replacement from a finite population, so each draw changes the remaining odds.

What are the argument constraints?

All four arguments are truncated to integers and must be non-negative. Each count must not exceed its container — for example population_s cannot exceed number_population — or the function returns an error.

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Related functions: HYPGEOM.DIST · BINOMDIST · NEGBINOMDIST · COMBIN · PERMUT