## 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
P( X = k ).

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 P(X=k) = h(k,n,m,r).

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