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Probability: The birth problem - mean and variance

  1. Oct 24, 2011 #1
    1. The problem statement, all variables and given/known data

    Suppose that a married couple in Canada decide to have babies until they get the first girl baby. It is well-known that in high-latitude countries, the chance of have a girl is slightly higher than the chance of having boy. Suppose that the chance of having a girl in Canada is 0.52. Let R be the ratio of boys to girls in the second generation for this family.

    a) Find the mean and variance of R
    b) What is the chance that there are more than 2 boy babies in the family?

    2. Relevant equations



    3. The attempt at a solution

    a) So the mean is E(X) of some random variable X. But R is a ratio. R is 48:52. How would R have a range if it is a ratio?
    b) Need to have 3 or more boys. So first 3 need to be boys: (48/100)^3
     
    Last edited: Oct 24, 2011
  2. jcsd
  3. Oct 28, 2011 #2

    vela

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    The couple ostensibly don't have any babies yet, so you don't know what the ratio will be, but you can calculate the expected value of the ratio.

    One random variable is N, the number of babies the couple will have. What is the distribution that describes N? If the couple has n babies, how many are girls and how many are boys? It's the latter number divided by the first number that is the ratio the problem is asking about.
     
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