You have N bags. Bag 1 has a black ball, Bag 2 has a black ball and a white ball, Bag 3 has a black ball and two white balls, and so on. Bag N has a black ball and N-1 white balls. You pick a ball from each bag at random and record the numbers of the bags that you picked a black ball from. For example, if you had 100 bags, then your sequence might be 1, 2, 3, 10, 14, 37. Call the last number in your sequence X. Prove that X is a random number from 1 to N with a uniform distribution.

(In reply to Simple enough by Jer)

I in no way mean the title of my previous comment to disparage the problem.  I consider it to be very simple and straightforward, but after all I teach probability. 

I definitely plan to start using this problem because it is a very cool result.

Posted by Jer on 2011-04-21 01:26:53