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January 12th, 2012, 02:52 AM  #11 
Newbie Joined: Jan 2012 Posts: 8 Thanks: 0  Re: mathematical expectation of how many times to get all ca
it takes at least 6 times to get all cards i think the expected values is 6*K6 + 7*K7 + ... + n*Kn Kn is possibility you get all cards at nth time. n>infinite 
January 12th, 2012, 04:20 PM  #12 
Global Moderator Joined: May 2007 Posts: 6,684 Thanks: 658  Re: mathematical expectation of how many times to get all ca
The problem statement is unclear. There are six cards. A card is picked at random. IS THE CARD PUT BACK??????????? If not, then the solution is the trivial one that I suggested. If it is put back, then it is an interesting problem.

January 12th, 2012, 05:38 PM  #13  
Newbie Joined: Jan 2012 Posts: 8 Thanks: 0  Re: mathematical expectation of how many times to get all ca Quote:
 
January 13th, 2012, 12:44 AM  #14  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: mathematical expectation of how many times to get all ca Quote:
So...is each card is marked uniquely and chosen with replacement? (i.e, when a card is chosen, is it put back in the group, possibly chosen again?) These are the kinds of things we need to know to solve the problem. A wellformed question gets a wellformed response...not being harsh, that's just the way it is...[color=#00BF00]mathman[/color] raises valid concerns that must be addressed before the question makes sense...otherwise people are really just guessing at what you mean. Help us to help you.  
January 13th, 2012, 08:50 AM  #15  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,955 Thanks: 988  Re: mathematical expectation of how many times to get all ca Quote:
1 take 6 cards at radom from a regular 52card deck 2 throw the other 46 in the garbage 3 pick a card (from the li'l pack of 6, of course; anyway the others are in the garbage...) 4 LOOK at the card, write down what it is 5 put it back in the li'l pack of 5 (so you now have 6), and shuffle 'em well 6 repeat steps 3 to 5 five more times (note that 5th step need not be done at end!) What is the probability that you wrote down 6 different cards?  
January 16th, 2012, 06:23 PM  #16  
Newbie Joined: Jan 2012 Posts: 8 Thanks: 0  Re: mathematical expectation of how many times to get all ca Quote:
i think this is what i mean.  
January 16th, 2012, 06:45 PM  #17 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,955 Thanks: 988  Re: mathematical expectation of how many times to get all ca
Well then, probability is: 6/6 * 5/6 * 4/6 * 3/6 * 2/6 * 1/6 = 5 / 324

January 17th, 2012, 02:27 PM  #18 
Global Moderator Joined: May 2007 Posts: 6,684 Thanks: 658  Re: mathematical expectation of how many times to get all ca
The problem statement originally was unclear. There are two different problems. 1) (Which has been answered) what is the probability that you will get six different cards when selecting six cards at random? 2) (Difficult) What is the average number of selections required to get six different cards? 
January 17th, 2012, 11:56 PM  #19  
Newbie Joined: Jan 2012 Posts: 8 Thanks: 0  Re: mathematical expectation of how many times to get all ca Quote:
sorry for my poor english. i think this is what i mean.  
January 18th, 2012, 01:40 AM  #20  
Newbie Joined: Jan 2012 Posts: 8 Thanks: 0  Re: mathematical expectation of how many times to get all ca Quote:
 

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