Date: Mar 20, 2013 10:43 AM
Author: mlookabaugh
Subject: Probability Question

Something that has been rattling around in my head for some time, and I just can't seem to get a handle on it.

What is the probability of selecting N numbers between 1 and 100 such that their sum is <=100 ?

Obviously N=1 is 1.0
For N=2, I've been trying to do something like calculate:

P(selecting 1) * P(selecting 99) +
P(selecting 2) * P(selecting 99 or 98) +
P(selecting 3) * P(Selecting 99, 98, or 97) +
...
P(selecting 99) * P(selecting 1)

That gets out of hand quickly with N>2. I could approximate a few values with code, but is there a way to get a closed form of this probability?

Any suggestions greatly appreciated.

Thank you,
Mark