## Binomial Distribution

For a b(k;n;p) distributed random variable X with fixed n and p you can calculate

• a histogram of the probabilities P( X = k )
• a table of their values from kmin to kmax
• the probability P( kmin < X < kmax)

### Theory:

n balls are drawn with replacement out of a container with a portion p of red balls. The random variable X stands for the amount of red balls drawn. The probability of k of the balls drawn being red, is characterized by P(X=k) = b(k;n;p).

The values for n and p are entered, where p as probability has to lie between 0 and 1. After this, a simple histogram gives a first survey over the values of P(X=k). The numeric values are issued in a table of values.

### Example:

```  n = 60;    p = .75

k           P(X=k)          P(0 ≤ X < k)
——    ——————   ——————
40      0,03834033      0,09248427
41      0,05610780      0,14859207
42      0,07614630      0,22473838
43      0,09562559      0,32036397
44      0,11083875      0,43120273
45      0,11822800      0,54943073
46      0,11565783      0,66508856
47      0,10335381      0,76844237
48      0,08397497      0,85241733
49      0,06169589      0,91411323
50      0,04071929      0,95483252
——    ——————   ——————
P(40 ≤ k < 50) =           0,90068858``` 