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>\displaystyle m/n,</math> where <math>\displaystyle m</math> and <math>\displaystyle n</math> are relatively prime positive integers, find <math>\displaystyle m+n.</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>\displaystyle m/n,</math> where <math>\displaystyle m</math> and <math>\displaystyle n</math> are relatively prime positive integers, find <math>\displaystyle m+n.</math> | ||
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| + | ==Solution== | ||
| + | {{solution}} | ||
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| + | ---- | ||
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| + | *[[Mock AIME 2 2006-2007/Problem 12 | Previous Problem]] | ||
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| + | *[[Mock AIME 2 2006-2007/Problem 14 | Next Problem]] | ||
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| + | *[[Mock AIME 2 2006-2007]] | ||
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== Problem Source == | == 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? [[Image:Razz.gif]] | 4everwise thought of this problem when watching Round 4 of the Professional Poker Tour. (What else can one do during the commercial breaks? [[Image:Razz.gif]] | ||
Revision as of 19:49, 22 August 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 
Solution
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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? 
