I disagree with Lee's answer

From: Mark Galecki (mgalecki@pacbell.net)
Date: Fri May 11 2001 - 00:36:13 MDT

Well, I don't know how extropian probability questions are and do they
belong on this list? Maybe they do, since they exercise our brains and thus
prevent Alsenheimer's...

Lee Corbin says:
> 2. A little girl's father discovers that his wife is
> pregnant again (but they don't know the sex of the
> unborn child). The man decides to visit a mathematician.
> "I have two children, sir", he says, "and one of them
> is a girl. What is the probability that the other is
> a boy?" What did the mathematician tell him?
> ***Answers*** For problems 1, 2, and 3, the answer is 2/3. For

I disagree with this one. (As you see I am trying to be diplomatic here
) ).

First, one of course assumes that sexes are equally probable (they aren't),
otherwise this would not be an interesting little problem.

One has to be careful about formulation of the problem. Lee wants to ask
"given that there is at least one girl, what is the probability that there
is one boy and one girl". The answer to this is of course 2/3, just as Lee

However, this is not what Lee is really asking. Note the pair of phrases:
"one", and "the other". What the father is really asking is "I have picked
one of my children (not necessarily at random). That child is a girl. What
is the probability that the other child is a boy". To this question the
answer is 1/2.

Mark Galecki

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