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 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?