Results 1 to 4 of 4

Math Help - Probability (drawing cards out of a set of 52)

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    3

    Probability (drawing cards out of a set of 52)

    Hey guys, I'm new here, but already have a question

    Basically, the task at hand is as follows. You have a set of 52 cards, out of which you randomly draw 8. What's the probability of an event that either a) three aces will be drawn or b) three kings will be drawn or c) three aces and three kings will be drawn.

    This is from a high school textbook and the solution says the said events are going to happen in (4 3)(48 5) + (4 3)(48 5) + (4 3)(4 3)(44 2). I get the first two, but I don't get why there is a plus in front of the third. Shouldn't there be a minus? I mean, the event c) is already covered in both the events a) and b), so if anything you should subtract that event so that it isn't counted twice. If my thinking isn't correct, what am I missing?

    Thanks in advance, everyone, I've been doing this problem for hours, but still can't figure out where I'm going wrong. Oh, and sorry for not using Latex, I'm not familiar with it. Those (4 3) etc. are supposed to represent binomial symbols, with 4 being "n" (at the top) and 3 being "r" (on the bottom).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    does (4 3) means {4 \choose 3}\; ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by Ryker View Post
    Hey guys, I'm new here, but already have a question

    Basically, the task at hand is as follows. You have a set of 52 cards, out of which you randomly draw 8. What's the probability of an event that either a) three aces will be drawn or b) three kings will be drawn or c) three aces and three kings will be drawn.

    This is from a high school textbook and the solution says the said events are going to happen in (4 3)(48 5) + (4 3)(48 5) + (4 3)(4 3)(44 2). I get the first two, but I don't get why there is a plus in front of the third. Shouldn't there be a minus? I mean, the event c) is already covered in both the events a) and b), so if anything you should subtract that event so that it isn't counted twice. If my thinking isn't correct, what am I missing?

    Thanks in advance, everyone, I've been doing this problem for hours, but still can't figure out where I'm going wrong. Oh, and sorry for not using Latex, I'm not familiar with it. Those (4 3) etc. are supposed to represent binomial symbols, with 4 being "n" (at the top) and 3 being "r" (on the bottom).
    I agree with you that the third term should be subtracted, not added. This is an example of the inclusion-exclusion principle.

    If they want a plus they could do

    \displaystyle \binom{4}{3}\bigg[\binom{48}{5}-\binom{4}{3} \binom{44}{2} \bigg] + \binom{4}{3}\bigg[\binom{48}{5}-\binom{4}{3} \binom{44}{2} \bigg] + \binom{4}{3}\binom{4}{3}\binom{44}{2}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jul 2010
    Posts
    3
    Thanks, I'm really glad to see I wasn't mistaken, though I hate the fact that I lost quite a lot of time over this just because the damn solution wasn't correct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 28th 2010, 05:58 PM
  2. Drawing cards...
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: September 27th 2010, 02:20 PM
  3. Probability of drawing cards.
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: September 17th 2010, 05:42 PM
  4. Probability(drawing cards)
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 3rd 2010, 12:07 PM
  5. Drawing cards out of deck
    Posted in the Statistics Forum
    Replies: 1
    Last Post: September 13th 2009, 01:06 PM

Search Tags


/mathhelpforum @mathhelpforum