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Comment by biotech | Hacker News Reader

"Some objected to the way I asked the question...."

Here Atwood links to a very insightful blog post by Paul Buchheit: http://paulbuchheit.blogspot.com/2009/01/question-is-wrong.h...

To continue the quote:

"...but it was a simple question asked in simple language."

Yes, a simple question, with two perfectly valid interpretations, as described by Buchheit. When I first read the question, I interpreted it the "wrong" way. The simple language that is used to ask the question is too simple, to the point of not being specific.

"I think what they're really objecting to is how unintuitive the answer is."

No sir. I am in fact objecting to the wording.

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I interpreted it the "wrong" way too. I thought about it like this: Instead of telling me that there is a girl or a boy tell me only that "1 + 1 = 2" and then ask me what the odds of the mothers child are for being a boy. I'll say 50%. I don't care what the state of some other child, I just care what the state of the unknown is. Now, if he had said, "you ask a woman that has a random assortment of children if she has at least 1 girl and she answers 'yes', what are the odds that the other is a boy" THEN I would be fine with the problem.

Paul's second algorithm, as stated, is exactly equivalent to the following:

1) Choose a random parent with exactly two children

2) If that parent has two boys, announce that they do not have two girls. If that parent has two girls, announce that they do not have two boys.

3) If that parent has a boy and a girl, randomly announce one of the above results.

It's easy to see that this has the same results as the first option. Counterintuitively, if that last step is nonrandom, you get the more intuitive result. Say, for example, that we did this:

1) Choose a random parent with exactly two children

2) Announce the gender of the eldest child.

This way, you get even odds that the other child is male or female. It's really counterintuitive, but that's how it works out.

Yudkowsky wrote a note about the same problem that cleared everything up for me: http://lesswrong.com/lw/ul/my_bayesian_enlightenment/

http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

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