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Hypergeometric Distribution

The hypergeometric distribution is a discrete distribution and is used to describe the probability to find k observations of class 1 when n objects are drawn from a population of N objects, and the probability of a single element of class 1 equals p.


N ... number of elements in population
n ... number of drawn samples
p ... probability of class 1
k ... observations of class 1

Graphical View
Applications Often used in quality control applications. 
First Moment m = np
Second Moment


Suppose you have 20 balls in a bag, 8 blue ones, and 12 red ones. Now mix the balls in the bag and draw 15 balls. What is the probability to draw exactly 5 blue balls and 10 red balls? The answer to this question is given by the hypergeometric distribution function:

N = 20
n = 15
p = 0.4 (8 of 20 balls are blue)
k = 5

The probability to draw exactly 5 blue balls is 0.238 as can be seen from the following distribution curve:

Last Update: 2005-Dez-31