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!

Question on probability

  1. Feb 26, 2006 #1
    Here's the question

    "In a faraway land long ago, boys were valued more than girls. So couples kept having babies until they had a boy. The frequency of boys and girls in the populations as a whole remained equal, but what was the expected frequency of girls per family? (Assume that each sex is equally likely)"

    I have a hint (see attachment)

    I kind of see what they want, but I don't really know how to get it. I tried to find the expected value for a given case (let's say they have n babies), but it doesn't really come out to what they have. I don't really know how the fact that the frequency of boys and girls remains equal fits into the problem, either.

    Any help is appreciated.
     

    Attached Files:

  2. jcsd
  3. Feb 26, 2006 #2

    StatusX

    User Avatar
    Homework Helper

    There's a couple ways to do this. First, you can just find the expected value of the number of girls in a family by <g>=0*p(0)+1*p(1)+..., where p(n) is the probability of a family having n girls. For example, p(0)=1/2 since there is a 50% chance the first child will be a boy and the family will stop after that.

    The other way is to note that the expected value of the number of boys per family is <b>=1, since a family won't stop until they have exactly one boy. Then the total number of boys is B=F*<b>=F, where F is the number of families. You also know B=G, ie, the total number of boys equals the total number of girls, (they tell you this, but do you understand why it is?), so what does this give you for <g>?
     
    Last edited: Feb 26, 2006
  4. Feb 26, 2006 #3
    This makes sense... but I don't get the same infinite sum that's given (I get n*x^(n+1) instead of x^(n+1)/(n+1).

    This makes sense too, but wouldn't that just give you 1 for <g>? And sorry, I don't understand why total number of boys has to equal total number of girls

    Thanks for taking the time to help, I really appreciate it
     
  5. Feb 26, 2006 #4

    0rthodontist

    User Avatar
    Science Advisor

    What is the probability that the first child a couple will have is a boy? Assuming the couple makes it to the second child, what is the probability the second child a couple will have is a boy? Assuming the couple makes it to the third child, what is the probability the third child a couple will have is a boy?
     
  6. Feb 26, 2006 #5

    StatusX

    User Avatar
    Homework Helper

    Yea, I get the same thing as you. I'm not sure what they were going for with that hint, maybe there's another way to do it. But you can evaluate the sum using the same basic method they did, only differentiating where they integrated.

    The reason is that the next child who's born (anywhere) is either a boy or a girl with equal probability.
     
  7. Feb 26, 2006 #6
    1/2 for all of them, correct?
     
  8. Feb 26, 2006 #7
    OK, well doing it both ways StatusX described I get 1 as an expected value. This seems to make sense to me, I don't really understand that hint but i'll just ignore it. Thanks for the help everyone!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Question on probability
  1. Probabilities question (Replies: 2)

  2. Probability Question (Replies: 5)

Loading...