Awhile back I bought 2 identical rolls of dental floss, each with 50 uses, and picked them randomly. Tonight, the one I picked hit the 50 use mark. What is the expected number of uses in the remaining roll? 

With a 100000 case brute force, I get an expected answer of 8 uses. Neat, so I have maybe a week.

[![dental floss graph](https://i.stack.imgur.com/gyULY.jpg)](https://i.stack.imgur.com/gyULY.jpg)

What is the non-brute force answer?