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Topic: probability question
Replies: 9   Last Post: Mar 13, 2008 4:08 PM

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quasi

Posts: 12,057
Registered: 7/15/05
Re: probability question
Posted: Mar 12, 2008 2:15 AM
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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.

If the father always chooses the younger child to go with him, then
there is no information, so the probability that the other child is a
girl is 1/2.

Similarly, if the father always chooses the older child to go with
him, then again there is no information, so the probability that the
other child is a girl is 1/2.

If a boy has _priority_ over a girl to go with the father, then the
probability that the other child is a girl is 2/3.

If a girl has _priority_ over a boy to go with the father, then the
probability that the other child is a girl is 0.

Thus, the probability critically depends on the selection mechanism.

In the absence of any information, the problem is not well posed.

Of course, in a given situation. you can always make a subjective
judgement as to the type of selection, in which case, you can then
derive an answer based on that extra assumption.

For example, thinking about it culturally, if I _had_ to guess, I
would guess that the father would choose to take the _younger_ child,
in which case, the probability is 1/2.

quasi



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