This routine randomly selects a number given a list of partial probabilities

*L₁* - The bin sizes of the partial probabilities

*C* - Which bin is selected

The variables used in the routine.

L₁, L₂, X, U, S, L, T, C,E

TI-83/84/+/SE/CSE/CE

```
L₁→L₂
sum(L₂→X
Xˉ¹→U
U→S
DelVar LDelVar C
rand→T
For(E,1,dim(L₂
While L₂(E) and not(C
If L≤T and U≥T
Then
E→C
Else
L₂(E)-1→L₂(E
U+Xˉ¹→U
L+Xˉ¹→L
End
End
End
C
```

This routine takes a single list, and randomly selects an element according to the bin sizes in the list. It copies the list so as to not overwrite the data. It then sums the list, and takes the inverse of the sum to use as an interval. It then generates a random number between 0 and 1. By testing if this number falls within the intervals defined by each partial probability, it determines which bin the random number falls into.

As an example, if the input is {4,11,2,3} there is a 4/20 chance that Bin 1 is chosen, an 11/20 chance for bin 2, 2/20 for bin 3, and 3/20 for bin 4. If a bin size is 0, it will be skipped and never selected as the probability is 0.

.