Families in a certain society choose the number of children that they will have

Question

Families in a certain society choose the number of children that they will have according to the following rule: If the first child is a girl, they have exactly one more child. If the first child is a boy, they continue to have children until the first girl, and then cease childbearing. For k = 0,1,2,..., what is the probability that a particular family will have k children in total? For k = 0,1,2,..., what is the probability that a particular family will have exactly k male children among their offspring?

Explanation / Answer

(a) p0 = p1 = 0; p2 = 3/4; pk = (1/2)k , k ? 3. (b) P(0 males)=1/4, P(1 male)=1/2, P(k males)= (1/2)k+1 , k ? 2.

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