Married couples - geometric distribution

  1. A couple plans to continue having children until they have their first girl. Suppose the probability that a child is a girl is 0.5, the outcome of each birth is an independent event, and the birth at which the first girl appears has a geometric distribution. What is the couple's expected family size? Is the geometric pdf a reasonable model?

    The expected value of a geometric dist. is 1/p = 1/0.5 = 2.

    My problem is the 2nd question: from my point of view.. my answer is yes. Bec. the even only concerns w/ success-girl and failure-boy. Is my reason enough to say that gd. is the reasonable model? =)
     
  2. jcsd
  3. mathman

    mathman 6,621
    Science Advisor
    Gold Member

    The probability that they will have n children (n >=1) is .5n. I presume that is a case of geometric distribution.
     
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