The other interpretation that leads to 1/3 probably is also pretty intuitive. That's the fun part of this question is that it leaves crucial information unspecified.

I think this is a reasonable interpretation:

You meet a family at a party. They say "We have two children". You ask "Do you have any girls"? They say "yes!"

This will give you 1/3 probability that the other child is also a girl.

I think this interpretation is more intuitive because it doesn't make any assumptions about how you get your information. Usually in probability questions you assume any information you have is given to you from on high. For example, you just "know" that the family has two children, you don't somehow deduce it. Therefore I assume the same for "one child is a girl" information.

> I think this interpretation is more intuitive because it doesn't make any assumptions about how you get your information.

Do you mean “interpretation” or “alternative problem”.

Because if it’s an “interpretation” of the original problem you’re indeed making assumptions to fill the unspecified information.

If you mean that it’s an alternative problem which has a definite solution I agree. It’s a different problem and its relevance to the original one is to illustrate that additional assumptions were required.