1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probability of drawing a full house

  1. Dec 16, 2012 #1
    1. The problem statement, all variables and given/known data

    What is the probability of drawing a full house from a standard deck (52).


    2. Relevant equations



    3. The attempt at a solution

    These are the two answers I came up with:

    (52/52) * (3/51) * (2/50)* (48/49) * (3/48) * 5C3 * 5C2 = 0.0144~

    or

    (52/52) * (3/51) * (2/50)* (48/49) * (3/48) * 5C3 = 0.00144~


    The second answer is the correct one.

    I know you multiply by 5 choose 3 because there are three matching cards that you need to select out of five spots.
    But what about the pair? Do I need to multiply by 5 choose 2?

    The simulation on Wolframalpha comes up with a probability that is close to my second answer.(The correct one).
     
  2. jcsd
  3. Dec 16, 2012 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The multiplication by 5C3 expresses that you don't care which of the 5 cards are the trio. But once that's decided, there are only two spots left for the pair, so you do not want to multiply by 5C2 as well. In fact, you could have done it either way round, 5C3 and 5C2 being the same.
     
  4. Dec 16, 2012 #3
    Oh, I see. So after the location of the first three cards are 'picked', the location of the other 2 cards have been determined. Or vice versa where the location of the pairs are determined first and then the three cards basically have no where else to go.
    Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook