Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By MathoMan

Math Help - This is a probability question that I don't quite understand

  1. #1
    Newbie Schuyla's Avatar
    Joined
    Apr 2012
    From
    Colorado
    Posts
    15

    This is a probability question that I don't quite understand

    In an attempt to reduce the growth of its population, China instituted a policy limiting a family to one child. Rural Chinese suggested revising the policy to limit families to one son. Assuming the suggested policy is adopted and that any birth is as likely to produce a boy as a girl, explain how to use simulation to answer the following:

    1. What would be the average family size?
    2. What would be the ratio of newborn boys to newborn girls?


    So if anyone can help explain this one, I would truly be grateful.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Sep 2010
    Posts
    185
    Thanks
    13

    Re: This is a probability question that I don't quite understand

    A family that would count n members would look like: n= 2parents + number of girls born + 1 son, or more precisely n=k+3, where k is the number of girls born prior to the birth of a son.

    First you set up a random variable X that would count the members of the family. Its values would be x_0=3=2+0+1, x_1=4=2+1+1, x_2=5=2+2+1, x_3=6=2+3+1, .... You get the pattern, right? x_k=k+3 where k is the number of girls born before the first son.

    Then you should assign probabilities to those values.
    p_k=P(X=k+3)=(0.5)^{k} \cdot 0.5 = (0.5)^{k+1}, where (0.5)^{k} means that the  k members are girls born prior to a son being born, and he is born with the probability 0.5. So you can
    So now you have
    X\sim\left(\begin{array}{ccccc}3 & 4 & 5 & 6 & \cdots \\ 0.5 & (0.5)^{2} & (0.5)^{3} & (0.5)^{4} & \cdots \end{array}\right)

    Next, find the expected value of that random variable:
    \sum\limits_{k=0}^{\infty}x_k\cdot p_k & =\sum\limits_{k=0}^{\infty}(k+3)(0.5)^{k+1}= \frac{1}{2} \sum\limits_{k=0}^{\infty}(k+3)(0.5)^{k}=
    =\frac{1}{2} \left(\sum\limits_{k=0}^{\infty}k(0.5)^{k}+3\cdot \sum \limits_{k=0}^{\infty}(0.5)^{k}\right)= \frac{1}{2}\left(2+3\cdot 2\right)=4.

    I think that would be the size of the average family, unless I'm wrong, eh?!
    Last edited by MathoMan; April 4th 2012 at 03:38 AM.
    Thanks from Schuyla
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie Schuyla's Avatar
    Joined
    Apr 2012
    From
    Colorado
    Posts
    15

    Re: This is a probability question that I don't quite understand

    Thank you for your explanation! I went a round about way of doing this and came up with my answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Probability question i dont understand
    Posted in the Statistics Forum
    Replies: 26
    Last Post: September 23rd 2010, 12:51 PM
  2. Replies: 0
    Last Post: February 27th 2010, 11:57 AM
  3. Don't understand the question?
    Posted in the Algebra Forum
    Replies: 5
    Last Post: July 23rd 2009, 08:06 AM
  4. Don't Understand the Question
    Posted in the Statistics Forum
    Replies: 5
    Last Post: February 3rd 2009, 12:48 PM
  5. Please help me understand the question
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: May 1st 2008, 08:02 PM

Search Tags


/mathhelpforum @mathhelpforum