HYPGEOM.DIST Function

Excel Functions › Statistical

Excel 2010+ Statistical

The Excel HYPGEOM.DIST function returns the hypergeometric distribution — the probability of drawing a given number of successes in a fixed sample drawn without replacement from a finite population.


Quick answer:
=HYPGEOM.DIST(1,4,8,20,FALSE) P(exactly 1 success) ≈ 0.3633

Syntax

=HYPGEOM.DIST(sample_s, number_sample, population_s, number_pop, cumulative)
ArgumentDescription
sample_sRequiredThe number of successes you want in the sample.
number_sampleRequiredThe size of the sample drawn.
population_sRequiredThe total number of successes in the population.
number_popRequiredThe size of the whole population.
cumulativeRequiredTRUE returns the cumulative probability (sample_s or fewer); FALSE returns the exact probability mass for sample_s.

How to use it

Use HYPGEOM.DIST for sampling without replacement — cards from a deck, defective parts in a shipment, marked fish in a lake. (When draws are with replacement, use BINOM.DIST instead.)

=HYPGEOM.DIST(1,4,8,20,FALSE) // exactly 1 of 8 in a sample of 4 from 20 ≈ 0.3633
=HYPGEOM.DIST(1,4,8,20,TRUE) // 1 or fewer ≈ 0.4654

Read the example as: a population of 20 contains 8 successes; you draw a sample of 4; what is the chance of getting exactly 1 success? Setting cumulative to TRUE sums the probabilities from 0 up to sample_s.

Binomial vs hypergeometric: if the population is very large relative to the sample, draws are nearly independent and the binomial distribution is a good approximation. For small finite populations, the hypergeometric is exact.

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Live demo

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Result:

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Frequently asked questions

What is the difference between HYPGEOM.DIST and BINOM.DIST?
BINOM.DIST assumes draws are independent — sampling with replacement or a constant success probability. HYPGEOM.DIST is for sampling without replacement from a finite population, where each draw changes the remaining odds.
What is the order of the arguments?
sample_s, number_sample, population_s, number_pop, cumulative — successes in the sample, sample size, successes in the population, population size, then the cumulative flag.
How is HYPGEOM.DIST different from the legacy HYPGEOMDIST?
The old HYPGEOMDIST (no dot) had no cumulative argument — it only returned the exact probability mass. HYPGEOM.DIST adds the cumulative flag so you can get cumulative probabilities too. HYPGEOMDIST still works for backward compatibility.
Why might HYPGEOM.DIST return an error?
It returns #NUM! if any argument is out of range — for example sample_s greater than number_sample, or population_s greater than number_pop. Non-numeric arguments return #VALUE!.

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Related functions: BINOM.DIST · BINOM.INV · NEGBINOM.DIST · POISSON.DIST · COMBIN