1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Probability Question - Urn problem

  1. Mar 31, 2013 #1
    1. The problem statement, all variables and given/known data

    An urn contains 4 white and 4 black balls. We randomly choose 4 balls. IF 2 of them are white and 2 are black, we stop. If not, we replace the balls in the urn and again randomly select 4 balls. this continues until exactly 2 of the 4 chosen are white. What is the probability that we shall make exactly n selections.

    2. Relevant equations

    3. The attempt at a solution

    I don't see why I can't find the probability of drawing exactly 2 white balls using this method.

    where 4C2 is 4 choose 2

    apparently this is wrong but I don't see why. Thanks for any help that you can provide.
  2. jcsd
  3. Mar 31, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    Well, why do you think it's right? The probability of choosing a white ball is only 1/2 the first time you choose a ball. It's not always 1/2, is it?
  4. Mar 31, 2013 #3
    oh i guess i always assumed you pick the things simultaneously as that's what I've been doing throughout the course so i guess this assumption is wrong?
  5. Mar 31, 2013 #4


    User Avatar
    Science Advisor
    Homework Helper

    If you pick a white ball first that means there are 3 whites left and 4 blacks. The odds of picking a second white or a black aren't 1/2 anymore. So yes, it's wrong.
  6. Apr 2, 2013 #5


    User Avatar
    Science Advisor

    I think it is always useful to describe the sample space: you can succeed the 1st, or the 2nd time, etc.

    EDIT: I mean, you can select the two balls in the first trial, or, if you don't, then at the second trial, etc.
    Last edited: Apr 2, 2013
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted