Results 1 to 2 of 2

Math Help - Simple problem...

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    1

    Simple problem...

    ... I'm having trouble with it anyway, even though I think it might just be high school review, so I wasn't entirely sure where to put this topic. Anyway:

    There are 15 items. Four are type A, five are type B, and six are type C. Selecting 3 randomly, what is the chance that exactly 2 will be type C?

    There is no item replacement and it's unordered.

    Since there are more questions using the same sort of thing later I was hoping to get a formula/method I could use with larger numbers instead of tracing through a diagram and multiplying every time.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jan 2010
    Posts
    8
    Looking at the categories:

    A: 4/15
    B: 5/15
    C: 6/15

    Now, looking at these possible outcome combinations: C,C,N ; C,N,C ; or N,C,C. (N denoting "not C" in this case.)

    This would be a simple binominal IF it were done with replacement:

    \binom{n}{k} p^kq^{n-k}

    But since there is no replacement, each succeeding factor is conditional to the previous factor (i.e. you simply remove what you take out at each step):

    Pr(2 C's | 3 Draws) = \binom{3}{2} (6/15)(5/14)(9/13)

    Where 9/13 is the "not C" part, i.e. 4/13 + 5/13
    Last edited by mr fantastic; January 26th 2010 at 02:31 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: February 11th 2011, 03:28 AM
  2. One more simple problem
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: May 28th 2010, 02:28 PM
  3. Simple Problem
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: May 28th 2010, 01:20 PM
  4. simple problem need help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 2nd 2009, 04:02 PM
  5. Simple problem... help please.
    Posted in the Geometry Forum
    Replies: 3
    Last Post: October 30th 2007, 02:40 AM

Search Tags


/mathhelpforum @mathhelpforum