[peakok]

Ok this thread is confusing. Actually, your second algorithm wasn't the point of my argument. You're right that according to your second formulation, the probability is 1/2, of course.

My point is that there is nothing wrong with Jeff's question, and I believed that you made a distinction with the Monty Hall version. But your second algorithm isn't the same as Jeff's question, my mistake.

It is very clear that my argument specifically adresses the question the way Jeff has formulated it, so you can even forget the part about "your second formulation", what I meant was the question of Jeff and why there is nothing wrong with it.

In statistics, it is commonly accepted that we don't know what we don't state (for an obvious practical purpose). Therefore, when we say : "One of them is a girl", it is implied that we don't know wich one because we didn't specify it.

Therefore there is nothing wrong with Jeff's question (and the probability is 2/3), at least for anyone familiar with basic statistics and probabilities conventions (and I suspect you are), anything else is just quibble. I assumed your argument wasn't about nitpicking this kind of convention, but it turns out I was wrong. I guess nobody wins this one :)

[randallsquared]

This hinges on whether we decided ahead of time that we would only consider cases in which there is a girl, something which I didn't see earlier. :)

As mentioned in another thread started by Eliezer, it's the difference between "What is the sex of one of your children?" and "Is (at least) one of your children a girl?". For the second question, the results skew to 1/3 and 2/3 because we're discarding the cases where the answer is 'no'.

The light went on for me when Paul pointed out in his update that getting a random answer for "What is the sex of one of your children?" eliminates (an unknown) one of BG and GB.

[peakok]

Basically you're right, and Paul is right too. This is just a matter of convention, it depends on what you want to hear in the question. If Jeff said "one of the children is a girl", but added "but we don't know wich one of the two is", this post would have never existed and we wouldn't have argued so much over nothing.

In the world of mathematical conventions you learn in school, the question is understood and you're right. In the "normal" world where you can quibble with language because there is no specific agreement, Paul is right and the question should be more precise. In both cases the conclusion remains the same : what a waste of time.