# Problem of the Week, #118

A colleague Bill Wardlaw (March 3, 1936-January 2, 2013) used to create a “Problem of the Week” for his students, giving a prize of a cookie if they could solve it. Here is one of them.

## PROBLEM 118

Suppose that you draw numbers $x_1,x_2,\dots$ from $[0,1]$ randomly until $x_1+x_2+\dots +x_n$ first exceeds $1$. What is the probability that this happens on the fourth draw? That is, what is the probability that $x_1+x_2+x_3 < 1$ and $x_1+x_2+x_3+x_4 > 1$?

## PROBLEM 118A

In the above problem, what is the expected number of draws until the sum first exceeds $1$?