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