quasi
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Registered:
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Re: probability question
Posted:
Mar 12, 2008 2:15 AM


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

