HYPGEOMDIST

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HYPGEOMDIST

Returns the hypergeometric distribution. HYPGEOMDIST returns the probability of a given number of sample successes, given the sample size, population successes, and population size. Use HYPGEOMDIST 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

HYPGEOMDIST(sample_s,number_sample,population_s,number_population)

Sample_s    is the number of successes in the sample.

Number_sample    is the size of the sample.

Population_s    is the number of successes in the population.

Number_population    is the population size.

Remarks

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

    Equation

    where:

    x = sample_s

    n = number_sample

    M = population_s

    N = number_population

    HYPGEOMDIST is used in sampling without replacement from a finite population.

Example

A sampler of chocolates contains 20 pieces. Eight pieces are caramels, and the remaining 12 are nuts. If a person selects 4 pieces at random, the following function returns the probability that exactly 1 piece is a caramel.

Sample_sNumber_samplePopulation_sNumber_PopulationFormula Description (Result)
14820=HYPGEOMDIST([Sample_s],[Number_sample],[Population_s],[Number_Population]) Hypergeometric distribution for sample and population (0.363261)