
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 10th, 2012, 09:37 AM  #1 
Newbie Joined: Jan 2012 Posts: 8 Thanks: 0  mathematical expectation of how many times to get all cards
there are 6 cards. a user picks a card from the 6 cards randomly each time. chance of getting each card is equal. what is the expected value of how many times a user get all of 6 cards? thanks in advance. 
January 10th, 2012, 01:20 PM  #2 
Global Moderator Joined: May 2007 Posts: 5,819 Thanks: 405  Re: mathematical expectation of how many times to get all ca
You need to clarify the process.

January 10th, 2012, 01:23 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 6,165 Thanks: 432  Re: mathematical expectation of how many times to get all ca
6/6 * 5/6 * 4/6 * 3/6 * 2/6 * 1/6 = 5 / 324 : with replacement, which is what I think you mean!

January 10th, 2012, 05:53 PM  #4 
Newbie Joined: Jan 2012 Posts: 8 Thanks: 0  Re: mathematical expectation of how many times to get all ca
sorry for my poor english. i wanted to know the expected value of how many times it takes for a user to get all cards. i think i just figured out the formula. 6 * (1/6)6 + 7 * C(6, 1) * (1/6)7 + 8 * (C(6,1) + C(6,2)) * (1/6)8 + ... + 11 * (C(6,1) + C(6,2) + C(6,3) + C(6,4) + C(,6,5)) * (1/6)11 + 12 * (2^6  1) * (1/6)12 + ... + n * (2^6  1) * (1/6)n C = combination (1/6)n = pow((1/6), n) 
January 10th, 2012, 09:24 PM  #5 
Newbie Joined: Jan 2012 Posts: 8 Thanks: 0  Re: mathematical expectation of how many times to get all ca
~= 63 * (1*(1/6) + 2*(1/6)^2 + ... + n*(1/6)^n) = 63 * 26 / 25 ~= 65 
January 11th, 2012, 09:48 AM  #6 
Newbie Joined: Jan 2012 Posts: 21 Thanks: 0 
I am asking for any books/ materials discussing the background of these formula (especially the mechanics, statistics, numerical method parts): http://www.mathsnetalevel.com/index.php ... I_formulae They look terrific. I don't find any nice book talking about this. I just learnt the solution in an educational TV. cards numbered 1, 2, 3, 4, 5, 6 In order to collect all cards: 1st trial: Any card could be chosen. P=6/6 The expectation of no. of trials=1 2nd trial: the card appeared in trial 1 is not allowed P=5/6 The expectation of no. of trials to obtain the other cards=6/5 3rd trial: the cards appeared in trial 1, trial 2 are not allowed P=4/6 The expectation of no. of trials to obtain the other cards =6/4 4nd trial: the cards appeared in trial 1, trial 2, trial 3 are not allowed P=3/6 The expectation of no. of trials to obtain the other cards =6/3 ... 6nd (last) trial: the 5 cards appeared in previous trials are not allowed. The probability to pick this card =1/6. We are expected to draw 6/1 times to get this card. trial expectation= 6/6+6/5+6/4+6/3+6/2+6/1 
January 11th, 2012, 04:13 PM  #7 
Global Moderator Joined: May 2007 Posts: 5,819 Thanks: 405  Re: mathematical expectation of how many times to get all ca
The process you described looks like picking cards at random without putting them back. All I see then is you pick 6 cards and get them all  there is no probability involved.

January 11th, 2012, 06:48 PM  #8  
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: mathematical expectation of how many times to get all ca Quote:
EDIT: Never mind. I just realized what I was quoting was not by the OP. Although I think that probably is a correct interpretation, like what Denis did.  
January 11th, 2012, 09:42 PM  #9 
Newbie Joined: Jan 2012 Posts: 21 Thanks: 0 
This problem is more difficult than it seems. Don't look down on it. I just remember the solution, and don't understand before. 
January 11th, 2012, 11:34 PM  #10 
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: mathematical expectation of how many times to get all ca
Who was looking down on it? Where'd that come from?


Tags 
cards, expectation, mathematical, times 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Expectation of Drawing Cards of the Same Suit  rubis  Advanced Statistics  5  January 5th, 2014 05:08 PM 
probabilitymathematical expectation  helloprajna  Math Books  0  November 18th, 2012 10:50 PM 
0 six times + 1 five times  Sara so  Algebra  3  January 4th, 2011 12:27 PM 
Mathematical cards + books  innovative educational goods  wkmrachmistrz  Math Books  0  September 18th, 2010 04:46 AM 
Mathematical Cards + Books  wkmrachmistrz  Math Books  0  August 22nd, 2009 01:32 AM 