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 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> | + | 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>m/n,</math> where <math>m</math> and <math>n</math> are relatively prime positive integers, find <math>m+n.</math> |
==Solution== | ==Solution== | ||
{{solution}} | {{solution}} | ||
| − | + | ==See also== | |
| − | |||
*[[Mock AIME 2 2006-2007/Problem 12 | Previous Problem]] | *[[Mock AIME 2 2006-2007/Problem 12 | Previous Problem]] | ||
Revision as of 11:03, 10 February 2008
Contents
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 
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
Problem Source
4everwise thought of this problem when watching Round 4 of the Professional Poker Tour. (What else can one do during the commercial breaks? 
