```Date: Mar 12, 2008 7:37 AM
Author: briggs@encompasserve.org
Subject: Re: probability question

In article <ajbft3p29adcp0sev30iojgbnsjhplqdl6@4ax.com>, quasi <quasi@null.set> writes:> On Wed, 12 Mar 2008 00:33:19 -0700, The World Wide Wade> <aderamey.addw@comcast.net> wrote:> >>In article <b1set3l134nn2kt3buh893q8jjfg3kau6s@4ax.com>,>> quasi <quasi@null.set> wrote:>>>>> On Tue, 11 Mar 2008 21:56:27 EDT, Steven <sgottlieb60@hotmail.com>>>> 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 streetcorner that you have a child at home conditioned on whether thatchild is a girl?What is the probability that you went out for a walk conditionedon the fact that the child that you selected based on a flip ofa coin might not want to go out for a walk?What is the probability that you walked by that particular cornerconditioned on the gender of the child that you actually did takefor a walk?
```