In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k successes (random draws for which the object drawn has a specified feature) in n draws, without replacement, from a finite population of size N that contains exactly M objects with that feature, wherein each draw is either a success or a failure. The hypergeometric distribution is also used to identify which sub-populations are over- or under-represented in a sample. Thus, it has a wide range of applications.

However, the probability for exactly k successful draws out of M draws is: \[ {\displaystyle p(k)=\ P(X=k)={\frac {{\binom {M}{k}}{\binom {N-M}{n-k}}}{\binom {N}{n}}}}\]

The classical model for this distribution is the Lottery “6 out of 49” example: N = 49 numbered balls are in an urn n = 6 balls are randomly drawn from the urn M = 6 numbers has been wagered k = 3,4,5,6 are successful event of the wagering

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The E-Learning project SOGA-R was developed at the Department of Earth Sciences by Kai Hartmann, Joachim Krois and Annette Rudolph. You can reach us via mail by soga[at]zedat.fu-berlin.de.

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You may use this project freely under the Creative Commons Attribution-ShareAlike 4.0 International License.

Please cite as follow: Hartmann, K., Krois, J., Rudolph, A. (2023): Statistics and Geodata Analysis using R (SOGA-R). Department of Earth Sciences, Freie Universitaet Berlin.