Results 1 to 4 of 4

Math Help - Trouble with a conditional probability problem

  1. #1
    Member
    Joined
    Oct 2009
    From
    Detroit
    Posts
    158
    Thanks
    5

    Trouble with a conditional probability problem

    Consider an urn containing 12 balls, of which 8 are white. A sample of size 4 is to be drawn with replacement (without replacement). What is the conditional probability (in each case) that the first and third balls drawn will be white given that the sample drawn contains exactly 3 white balls?

    So I'm having some trouble with the version of this problem that requires replacement.

    Let, E be the event that the first and third draws are both white balls, and F be the event that the sample contains exactly 3 white balls.

    So I'm looking for the conditional probability of E given F which is;


    Where the intersection is the probability of drawing 1 non-white ball and 3 white balls. And since there are two valid permutations (wwwn,wnww) we introduce a factor of two


    My problem is with the probability of F; which I'm defining as the odds of drawing one non-white ball and 3 white balls. I'm getting an answer that is less then the intersection of E and F so it's clearly nonsense.

    Do I need to permute the balls in F or something?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,677
    Thanks
    1618
    Awards
    1

    Re: Trouble with a conditional probability problem

    Quote Originally Posted by bkbowser View Post
    Consider an urn containing 12 balls, of which 8 are white. A sample of size 4 is to be drawn with replacement (without replacement). What is the conditional probability (in each case) that the first and third balls drawn will be white given that the sample drawn contains exactly 3 white balls?
    Let's look at the condition: "given that the sample drawn contains exactly 3 white balls".
    That means we can cut down on the space to these events.
    BWWW, WBWW, WWBW, WWWB
    How many of those have a white in the first and third place?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2009
    From
    Detroit
    Posts
    158
    Thanks
    5

    Re: Trouble with a conditional probability problem

    Quote Originally Posted by Plato View Post
    Let's look at the condition: "given that the sample drawn contains exactly 3 white balls".
    That means we can cut down on the space to these events.
    BWWW, WBWW, WWBW, WWWB
    How many of those have a white in the first and third place?
    Just the two. I'm not sure where this is going unless I just need to double that again?



    ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Oct 2009
    From
    Detroit
    Posts
    158
    Thanks
    5

    Re: Trouble with a conditional probability problem

    Quote Originally Posted by Plato View Post
    Let's look at the condition: "given that the sample drawn contains exactly 3 white balls".
    That means we can cut down on the space to these events.
    BWWW, WBWW, WWBW, WWWB
    How many of those have a white in the first and third place?
    Oh no the conditional probability must be one half.

    So then how do I show that using the conditional probability formula?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: September 22nd 2012, 06:14 PM
  2. conditional probability problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 15th 2012, 01:17 AM
  3. Replies: 2
    Last Post: October 4th 2011, 12:56 PM
  4. Conditional Probability Problem
    Posted in the Statistics Forum
    Replies: 3
    Last Post: February 16th 2011, 05:43 PM
  5. Urn problem - conditional probability
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: September 10th 2008, 10:45 PM

Search Tags


/mathhelpforum @mathhelpforum