## Hyper geometric Distribution

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

This routine is especially useful, because hardly any tables for hyper geometric distribution exist due to the four input variables, and the calculation of probabilities requires a great deal of expenditure.

### 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 were drawn. The probability of k of the balls
drawn being red, is characterized by

The amount of balls drawn n, the total amount m and the amount of red balls r are entered. As the drawing proceeds without discarding, verify 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