Results 1 to 7 of 7

Math Help - cards

  1. #1
    Member billym's Avatar
    Joined
    Feb 2008
    Posts
    183

    cards

    4 players are dealt 13 cards from a 52 card deck. What is the probability that one player gets exactly 3 aces?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,385
    Thanks
    1475
    Awards
    1
    Quote Originally Posted by billym View Post
    4 players are dealt 13 cards from a 52 card deck. What is the probability that one player gets exactly 3 aces?
    There are \frac{52!}{(13!)^4} ways deal 13 cards to each of 4 players.

    There are \binom{4}{3}\binom{48}{10} to deal one hand with exactly 3 aces.

    Can you finish? (Donít forget the other three players.)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member billym's Avatar
    Joined
    Feb 2008
    Posts
    183
    I know the answer is 0.041 but i just cant get it...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member billym's Avatar
    Joined
    Feb 2008
    Posts
    183
    Shouldn't the total number of hands be \binom{52}{13} ?

    In which case it would be:

    (number of 3 ace hands) / (total number of hands):

    <br />
\binom{4}{3}\binom{48}{10}/\binom{52}{13} = 0.041<br />




    Last edited by billym; July 18th 2009 at 04:08 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,385
    Thanks
    1475
    Awards
    1
    Quote Originally Posted by billym View Post
    I know the answer is 0.041 but i just cant get it...
    I completely disagree with that answer.
    That is the probability that a particular player gets exactly three aces.
    The probability that some player gets exactly three aces is four times that number.
    You need to show this to whoever set this problem.
    That answer is wrong.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member billym's Avatar
    Joined
    Feb 2008
    Posts
    183
    I guess I worded it wrong. The full question is:

    "Consider a single hand of bridge. What is the probability for the hand to have exactly 3 aces?"

    Oops.

    What would the equation be if the question was the probability of some player getting 3 aces?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,385
    Thanks
    1475
    Awards
    1
    Quote Originally Posted by billym View Post
    I guess I worded it wrong. The full question is:
    "Consider a single hand of bridge. What is the probability for the hand to have exactly 3 aces?"
    Worded like that, then the text's given answer is correct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. probability of 5 correct cards out of 6 cards
    Posted in the Statistics Forum
    Replies: 8
    Last Post: May 20th 2011, 06:44 AM
  2. Replies: 2
    Last Post: October 2nd 2010, 03:09 PM
  3. 12 Cards are delath from 52 playing cards
    Posted in the Statistics Forum
    Replies: 7
    Last Post: November 13th 2009, 10:36 AM
  4. 2 same cards
    Posted in the Statistics Forum
    Replies: 8
    Last Post: October 27th 2009, 01:54 PM
  5. deals of n cards for all cards appear once
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 7th 2007, 07:26 AM

Search Tags


/mathhelpforum @mathhelpforum