## Hypergeometric Distribution

For a h(k;n;m;r) distributed random variable X with fixed n, m and r you can compute a histogram and a table of values for the probabilities

This routine is paticularly useful because, due to the four input variables, there are hardly any tables for the hypergeometric distribution and the calculation of probabilities requires a great deal of effort.

### Theory:

A container is filled with m balls, r of which are red. If n balls are drawn without replacement,
then the random variable X tells, how many red balls have been drawn. The probability that k of the balls
drawn are red, is given by

The number of balls drawn n, the total number m and the number of red balls r are entered. Since the drawing proceeds without discarding, it is checked that n<m, and also r<m.

### Example:

n = 20; m = 100; r = 50 k P(X=k) P(0 ≤ X < k) —— —————— —————— 5 0,00889760 0,01141749 6 0,02780501 0,03922250 7 0,06613084 0,10535334 8 0,12160243 0,22695577 9 0,17460862 0,40156439 10 0,19687122 0,59843561 11 0,17460862 0,77304423 12 0,12160243 0,89464666 13 0,06613084 0,96077750 14 0,02780501 0,98858251 15 0,00889760 0,99748011 —— —————— —————— P(5 ≤ k < 15) = 0,99496023