HYPGEOMDIST function

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.

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

  1. Create a blank workbook or worksheet.

  2. Select the example in the Help topic.

    Note   Do not select the row or column headers.

    Selecting an example from Help

    Selecting an example from Help

  3. Press CTRL+C.

  4. In the worksheet, select cell A1, and press CTRL+V.

  5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

1

2

3

4

5

A

B

Data

Description

1

Number of successes in the sample

4

Sample size

8

Number of successes in the population

20

Population size

Formula

Description (Result)

=HYPGEOMDIST(A2,A3,A4,A5)

Hypergeometric distribution for sample and population above (0.363261)

Applies To: Excel 2007



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