Mock AIME 2 2006-2007 Problems/Problem 13
Problem
In his spare time, Richard Rusczyk shuffles a standard deck of 
playing cards. He then turns the cards up one by one from the top of the deck until the third ace appears. If the expected (average) number of cards Richard will turn up is 
where 
and 
are relatively prime positive integers, find 
Problem Source
4everwise enjoys playing and watching card games. In fact, he thought of this problem when watching Round 4 of the Professional Poker Tour. (Guy caught an Ace on the river.)
