In article <email@example.com>, quasi <firstname.lastname@example.org> writes: > On Wed, 12 Mar 2008 00:33:19 -0700, The World Wide Wade > <email@example.com> wrote: > >>In article <firstname.lastname@example.org>, >> quasi <email@example.com> wrote: >> >>> On Tue, 11 Mar 2008 21:56:27 EDT, Steven <firstname.lastname@example.org> >>> wrote: >>> >>> >Suppose you meet me on a street corner and I introduce you to my son who is >>> >with me. I inform you that I have another child at home. What is the >>> >probability that my other child is a girl. >>> >>> The problem is not adequately specified. >>> >>> It depends on how the child accompanying the father is selected. >>> >>> If the child that accompanies the father is selected at random by a >>> flip of a fair coin, then the probability that the other child is a >>> girl is 1/3. >> >>The sample space for the children is (b b), (b g), (g b), (g g) where >>the first slot is the youngest child, the second slot is the oldest. >>These oredered pairs all have probability 1/4. Now we select a child >>at random for a walk. We get a new sample space: (b b b), (b g g), (b >>g b), (g b g), (g b b), (g g g), with the probabilities being 1/4 for >>the first and last triples, and 1/8 for the others. The probability >>the other child is a girl given the randomly selected child out with >>daddy is a boy is thus >> >>p((b g b) (g b b))/p((b b b) (b g b) (g b b)) >> >> = (1/8 + 1/8)/(1/4 + 1/8 + 1/8) = 1/2. > > Even without calculation, I should have realized my error based on the > following intuitive idea ... > > If there is no gender bias in the method by which the child who went > with the father is selected, then there can be no gender bias for the > child who wasn't selected.
You missed other places for bias to show up.
What is the probability that you will tell a stranger on a street corner that you have a child at home conditioned on whether that child is a girl?
What is the probability that you went out for a walk conditioned on the fact that the child that you selected based on a flip of a coin might not want to go out for a walk?
What is the probability that you walked by that particular corner conditioned on the gender of the child that you actually did take for a walk?