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January 3rd, 2014, 05:28 AM  #1 
Newbie Joined: Nov 2013 Posts: 20 Thanks: 0  Expectation of Drawing Cards of the Same Suit
In the 52 card deck, what is the expected number (average in the long run) of drawings you have to make to get k cards of the same suit, with or without replacement? 
January 3rd, 2014, 11:33 AM  #2 
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733  Re: Expectation of Drawing Cards of the Same Suit
With replacement it is trivially 4k. Without replacement it is more work to calculate, although for k > 13, it is impossible. 
January 3rd, 2014, 11:54 PM  #3 
Newbie Joined: Jan 2014 Posts: 2 Thanks: 0  Re: Expectation of Drawing Cards of the Same Suit
Nice post!

January 5th, 2014, 05:52 AM  #4 
Newbie Joined: Nov 2013 Posts: 20 Thanks: 0  Re: Expectation of Drawing Cards of the Same Suit
mathman, why don't you give the solutions, not only the answer.

January 5th, 2014, 07:36 AM  #5  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039  Re: Expectation of Drawing Cards of the Same Suit Quote:
thus he does not have enough time, having to drive a taxi in order to make up reduced income...  
January 5th, 2014, 04:08 PM  #6  
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733  Re: Expectation of Drawing Cards of the Same Suit Quote:
 

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