
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 8th, 2014, 03:38 AM  #1 
Newbie Joined: Dec 2010 Posts: 8 Thanks: 0  Card combinatorics and probabilities
Suppose there is a number K of cards in a deck, a majority L of which are black and a minority (KL) of which are red. Suppose that we draw one card at a time and after we've recorded the result, we put the card back into the deck and reshuffle it. Furthermore, suppose that one team, Team Black, wins if a majority of the drawn cards are black, and that the other team, Team Red, wins if a majority of the drawn cards are red. Draws are not allowed so if the two teams draw the same number of cards, we flip a coin to determine who wins. Suppose we draw N cards. It is obvious that the greater K is, the greater is the chance that Team Black will win, and that N approaches 1 in the limit. The formula (where N is odd) is given on p. 264 of this paper: http://www.socsci.uci.edu/~bgrofman/69% ... 0truth.pdf But suppose now that we instead use an alternative procedure. According to this procedure, if we encounter a card that already has been drawn (say the ace of spades or the ace of hearts), we don't count that card (though we do put it back in the deck). My conjecture is that this will not change the probability that Team Black will win (it holds for N=3, if I've calculated correctly). However, I can't prove this generally. Any help with this would be much appreciated. Please ask if anything's unclear. 
March 8th, 2014, 04:46 AM  #2  
Newbie Joined: Dec 2010 Posts: 8 Thanks: 0  Re: Card combinatorics and probabilities
Sorry it should not say Quote:
Sorry about this. There is no way of modifying posts after posting here, right?  

Tags 
card, combinatorics, probabilities 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
composed probabilities and total probabilities  RifkiNada  Algebra  2  November 24th, 2012 03:32 AM 
Card fun  Denis  Algebra  31  June 16th, 2012 05:59 AM 
Card game Combinatorics  eternity  Algebra  1  August 6th, 2010 12:46 PM 
"Pick a card, any card" probability question  Niko Bellic  Probability and Statistics  1  March 18th, 2010 01:15 PM 
Card box  bernando  Applied Math  2  July 3rd, 2007 06:21 PM 