Yes, we have gone over and over it, but I've been spurred to attempt to make my point again.
I will agree that the answer is supposed to be 1/3;1/3 is the answer the judges are looking for. But as the puzzle is written, the answer is 1/2.
The puzzle is written as:
"Ok, so Teanchi and Beanchi are a married couple (dont ask me whose he and whose she)!
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."
The puzzle should have been written as:
Ok, so Teanchi and Beanchi are a married couple (don't ask me who's he who's she)!
They have two kids. At least one of the kids is a girl. What is the probability that both kids are girls?
Assume safely that the probability of each gender is 1/2."
There is a big diffence between the two puzzles above (aside from spelling and grammar mistakes).
The way the puzzle was presented, we are asked the probability of one child. That "other kid". The probability of any "other kid" being a girl is 1/2.
The way the puzzle should have been presented, the answer is 1/3. The way it should have been presented makes the gender of both children a variable.
The way it was presented makes the gender of only one of the kids a variable. Not a particular kid, as I may have previously indicated, but one of them. Take yer pick!
In the simplest terms, the 1/3 camp has come to their answer using the gender of both kids as variable. As a member of the 1/2 camp, I have come to my answer using the gender of only one kid as variable. Just as the question asks: "What is the probability the other kid is also a girl."
I don't care which of the kids is the "one of them" girl. We are asked about the probability of "the other kid."
We are never asked about the probability of both kids being girls.
(By the by, I think this is a great puzzle, and a great forum. Thanks.)
Ok guys, I was willing to let it go, but now I've been forced to reach into my bag of tricks and open up a can of logical whup-a** on you all.
"One of them is a girl. What is the probability the other kid is also a girl?"
"One of them." "The other kid."
"One of them." "The other kid."
I'm not saying the OP assigned one of the children to be a girl. The question itself assigns one of them.
Seems clear to me:
There is "one", and there is the "other." We are asked about the probability of "The other kid."
I don't care if it's the first or the second born. I don't care how you look at it: "One of them is a girl." As soon as you ask about "the other" you've made that "other" the subject of the probability.
And the probability of "the other one" being a girl is 1/2.
I would guess it has something to so with him starting in, say, Hawaii or Alaska, and flying at a precise speed before landing in specific locations. Maybe the earth's rotation affecting his southward bearing?
A question for you: If the first sock happens to be a white one, and you put it back does the next sock picked count as the 2nd draw, or the 1st? I'm assuming that you mean it to count as the 2nd. And so on....
I've read your explanation and the rest of the thread. And I know how the answer is supposed to be 1/3 But...
It does come down to the wording.
"One of them is a girl"
"One of which is a girl"
The statement in the riddle is not "One of which" though. Nor is it "At least one of them is a girl"
It's a matter of assigning. As soon as you say "one of them" you've assigned, say, the first born, or the second born to be a girl. If one of them, say the first born, is in fact a girl, the chances of the other being a girl are 50%.
it does look to be 1/3. But, by assigning, by saying "one of them is a girl" I submit that you can, in a way, add a second G/G set.
Or, of those 6 kids, 4 are girls. The chances of "one of them" girls having a sister is 50%.