What's the probability that n random numbers from [0,1] will sum less than 1?

(For purists: "uniformly distributed, independent" random numbers are assumed.)

(In reply to simulation results by Charlie)

Oh, yes, I left out the rows for n=1 and n=2 as in those cases it is seen the probabilities are 1/1 and 1/2 respectively (the latter by symmetry  of <1 with >1), and those denominators are 1! and 2! respectively.

Posted by Charlie on 2004-07-29 09:00:40