Date: Mar 12, 2008 7:37 AM
Subject: Re: probability question

In article <>, quasi <quasi@null.set> writes:
> On Wed, 12 Mar 2008 00:33:19 -0700, The World Wide Wade
> <> wrote:

>>In article <>,
>> quasi <quasi@null.set> wrote:

>>> On Tue, 11 Mar 2008 21:56:27 EDT, Steven <>
>>> 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?