Subject: Re: Gender probabilities in a family with two children
Date: Sat 2/6/99 10:45 PM
From: Alex Bogomolny
Do yourself a favor and search my site for the Monty Hall dilemma. Quite relevant to your question.
I assume that, for a single child, the probabilities of being a boy or a girl both equal 1/2. Furthermore, I assume that, the number of children in a family does not affect their gender. I.e., the sex of any child is independent of the sex of other children.
With two children the are 4 possible combination: gg, gb, bg, bb. (The older is counted first.) When you say that one of the kids is a girl, you invalidate the bb combination. Only three remain: gg, gb, bg. In two out of three remaining combinations there is a boy. Hence the probability that the other child is a boy is 2/3.
When you see one girl and know for sure that the woman has another child, the probability that this other kid is a boy is 1/2 by the second of my assumptions: the sex of any child is determined independently of the sex of other children. Now, you do not consider a combination of two kids, but just one child who is a boy with the probability of 1/2.
All the best,