Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 13"
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== Problem == | == Problem == | ||
| − | In his spare time, Richard Rusczyk shuffles a standard deck of | + | In his spare time, Richard Rusczyk shuffles a standard deck of 52 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 <math>\displaystyle \frac{m}{n},</math> where <math>\displaystyle m</math> and <math>\displaystyle n</math> are relatively prime positive integers, find <math>\displaystyle m+n.</math> |
== Problem Source == | == 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.) | 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.) | ||
Revision as of 23:30, 24 July 2006
Problem
In his spare time, Richard Rusczyk shuffles a standard deck of 52 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.)
