Sorry, but I really have to take issue with this. I would say that the English language is imprecise in general because of how it developed. So just because you think there is an ambiguity in the phrasing, I don't think that should mean that the OP has multiple correct interpretations (or rather, that you interpretation is more correct than the mathematical community's consensus. )
This was the only concession I was seeking from the 1/3 fraternity.
That due to semantical interpretation it is possible to arrive at an alternative answer because of the ambigiuty in the wording of the puzzle
and that if you deconstruct the sentence it is possible to arrive with 1/2.
I have given numerous examples where the answer is 1/3, but the wording in our puzzle is sufficiently ambiguous to be open to semantical interpretation and therefore it is only possible to give a "best" answer. In this case I believe the "best" answer is 1/2.
Here is the exact wording:
"They have two kids, one of them is a girl, what is the probability that the other kid is also a girl.
Assume safely that the porbability of each gender is 1/2."
Now forgive me if I haven't been following this thread from beginning to end (I hope you can understand why:P) so this might have been used before, but as I read that sentence, I see an equivalent sentence that reads:
"They have two kids. Given that one of them is a girl, what is the probability that the other is also a girl?
Assume safely that the probability of each gender is 1/2."
This is conditional probability. Let's give the two kids gender-unspecific names, Kelly and Jean (abbreviated k and j) and say that "k is a girl" (G). Say that the event that "j is a girl" is A. The OP is asking for Pr(A|G). For the two events to be statistically independent, then Pr(A|G) = Pr(A). We know that this is not the case because if you know that one of them is a girl, that affects the choices for what the other child can be. This is why the answer should be 1/3, not 1/2.
1. Pr(A) = 1/2 (Given from OP)
2. Pr(A|G) = 1/3 (30 pages of explanation)
3. Pr(A|G) != Pr(A) (see 1 & 2)
If you can show that these two sentences have different semantic meanings, then I'll accept your answer, but as it is, I don't see that being the case.
Original: They have two kids, one of them is a girl, what is the probability that the other kid is also a girl?
Mine: They have two kids. Given that one of them is a girl, what is the probability that the other is also a girl?
Are they different?