Results 1 to 4 of 4

Math Help - Conditional probability - family with blue eyes

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    2

    Conditional probability - family with blue eyes

    Hi all,

    I'm looking for an answer to the following exercise. I've worked on some but I'm stuck. There is a family with 5 children, and the probability that any child will have blue eyes is 1/4. If you know that at least 1 has blue eyes, what is the probability that 3 or more have blue eyes? (I think I got this part, below.) The next part is: if you know that the youngest child in the family has blue eyes, what is the probability that 3 or more have blue eyes. Supposedly these answers are different.

    I think for the first part you can say that the probability than n children have blue eyes is:

    P_n = {5 \choose n}\frac14^n\frac34^{5-n}

    So the answer to the first part is, I think, a conditional probability:

    {P_3 + P_4 + P_5 \over P_1+P_2+P_3 + P_4 + P_5} = \frac{106}{781}

    The textbook has the answer for the second part as .25. But I don't see it. It seems to me you could just ignore the youngest child, and treat it now like a family of four and get the probability of 2, 3, or 4 children having blue eyes. But that's not .25, unless I'm calculating wrong (I get 67/256).

    Thanks for any help, take care,
    Rob
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    you got the first part correct..

    for the second one:

    At least 3 have blue eyes if and only if at least 2 of the other 4 have blue eyes. You can add the probabilities of these outcomes:

     6 \left(\frac{1}{4}\right)^{2} \left(\frac{3}{4}\right)^{2}+4\left(\frac{1}{4}\ri  ght)^{3} \frac{3}{4}+\left(\frac{1}{4}\right)^4
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2010
    Posts
    2
    You're result is also 67/256. Perhaps this textbook (Degroot Probability and Statistics, 3rd ed) is wrong. The back of the book says .25.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    As far as I know, it should be 0.26
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: July 22nd 2011, 01:39 AM
  2. Conditional Probability using the Law of Total Probability
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 7th 2010, 03:01 AM
  3. Replies: 4
    Last Post: June 9th 2009, 08:56 AM
  4. eyes
    Posted in the Math Challenge Problems Forum
    Replies: 13
    Last Post: February 7th 2008, 10:44 PM
  5. Probability: Red or Blue
    Posted in the Statistics Forum
    Replies: 2
    Last Post: March 20th 2007, 07:19 AM

Search Tags


/mathhelpforum @mathhelpforum