Re: Two children paradox

From: N. Silver (mathelp_at_worldnet.att.net)
Date: 11/08/04 

Date: Mon, 08 Nov 2004 18:21:42 GMT

Chan-Ho Suh wrote:

> Unfortunately, you've made an error in your analysis.
> We are not "stuck with BB, BG, GB". Clearly BG and
> GB cannot both be possibilities. You've seen one child.
> That child cannot be both male or female (for the purpose
> of this mathematical problem, of course). It is irrelevant
> whether you know which is older.

We start with the premise that Mr. Smith has
two children, which gives us these 4 equally-
likely possibilities: {BB, BG, GB, GG}.

Then we find out that at least one of Smith's children
is a boy, which restricts the space to 3 equally-likely
remaining possibilities: {BB, BG, GB}, which is an
"or" statement, not an "and" statement.

It's lucky that I'm not Marilyn Savant, because in that
case you would have egg on your face.

> So the possible sample spaces, if the observed child is male,
> are {BB, BG}, or {BB, GB}. The probability of the
> unobserved child being female is 1/2.

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