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March 12th, 2012, 09:57 PM  #1 
Senior Member Joined: Apr 2008 Posts: 194 Thanks: 3  how to solve this card game probability problem
In the game of bridge, four players are dealt 13 cards each from a wellshuffled deck of 52 playing cards. What is the probability that one of the players holds a hand that is made up of only one suit? my attempt let C represent combination There are 52C13 ways to choose any 13 cards. Since there are 4 players, each player has an equally likely chance to get only on suit. So, I multiply 1/52C13 by 4. Thus, my answer is 4/52C13. My friend says that my answer is wrong. So, how do you do it. Please help. 
March 12th, 2012, 10:02 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: how to solve this card game probability problem
What about the 4 ways for each player to get only one suit, since there are 4 suits?

March 12th, 2012, 10:52 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,417 Thanks: 1025  Re: how to solve this card game probability problem
4 / (52 C 13) I think! 
March 12th, 2012, 11:06 PM  #4 
Senior Member Joined: Jan 2012 Posts: 131 Thanks: 0  Re: how to solve this card game probability problem
52C13 ways, but 4 ways are similar suit. Each draw has probability of 4/52C13 of similar suit . 4 draws(4 persons)= 16/52C13 
March 13th, 2012, 09:03 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,417 Thanks: 1025  Re: how to solve this card game probability problem
Hmmm...isn't it same as player being dealt 13 cards consecutively? S0: 1 * 12/51 * 11/50 * ..... * 2/41 * 1/40 = ~.000000000006299078 Which is same as 4 / (51C13). 
March 13th, 2012, 09:17 PM  #6  
Senior Member Joined: Dec 2011 Posts: 277 Thanks: 1  Re: how to solve this card game probability problem Quote:
I think we should also make sure that the other three players must not hold cards of same suits as well. My very rough calculation gives an approximate answer of I'll explain more if you think my answer looks right to you. (Edit: I'm sorry, my figure seems wrong (but it must be an extremely small value)! Again, if you think I'm on the right track, I can give you the overall concept and idea because I don't think I have time to do it now. )  
March 14th, 2012, 03:52 AM  #7 
Senior Member Joined: Jan 2012 Posts: 131 Thanks: 0  Re: how to solve this card game probability problem
This is the same question taken from a book. In the game of bridge, each of 4 players is dealt 13 cards from an ordinary wellshuffled deck of 32 cards. Find the probability that one of the players(say, the eldest) gets a complete suit. ans: 4/52C13. Here the question emphasized on ONE. Thus the probability= 4C1/52C13= 4/52C13. Let the eldest player no2. xHxxxxxx.... xSxx xxxxx.. xDxxxxxxx... xCxxxxxxx.... >52C13 points The probability of all players get a complete suit must be 4C4/52C13=1/52C13 
March 14th, 2012, 08:36 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,417 Thanks: 1025  Re: how to solve this card game probability problem
Aziz, can you show that "clearly" by using only 12 cards: 3 of each suit.


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