Best...Puzzle...Ever....

[MerakSpielman]

Giving up on the spoilering, eh? Forgive if I keep at it a bit longer.

Spoiler

You are assuming, I think, that you know which child it is (first or second) after I tell you one is a boy. I haven't told you that, however. For the purposes of this excercise, shall we assume the order is birth order (first is older)? In that case, if I told you "my oldest child is a boy" the probability would be 50% as to the gender of the second child. In fact, the probability for the second child is always 50% once we fix the order. The problem here is that the order was not fixed when I told you that one is a boy. I can give you either child (older or younger) as the boy in the question provided. Like the Monty example, my choice of which child to reveal is not random.

. . . . . . . -- Eric

It doesn't matter. If the older child is a boy or if the younger child is a boy, you still have a 50-50 chance for the remaining child to be a girl or a boy. The Monty example only comes into play if the sex of the remaining child is not, in fact, random, but Monty knows and is keeping it a secret.

 

[MerakSpielman]

Pennstud, I was serious about my bet. Choose someone impartial on this board to be the diceroller, do fifty trials, and my bet (I'll increase it to fifty bucks to sweeten the pot) is that your end result will be closer to 2/3 correct if you always choose girl.

Daniel

Your bet is not an accurate depiction of the odds. My coin-flipping bet is.

I'll bet you any sum you choose that the result of the second flip of a coin is in no way changed by the result of the first flip, which is, in the end, what all your arguments are saying.

 

[Pielorinho]

No, your coinflipping isn't. Because time is one way, once you flip the coin once, that's the older flip; by flipping it, it's equivalent to saying that the OLDER child is a boy.

We're looking at a family where both kids' genders are already determined, where the coinflips have already happened.

That's very different.

Explain, please, why my bet is not an accurate depiction.
Daniel

 

[Piratecat]

Shall I throw some more oil on the fire?

Marilyn Ignores the Obvious Regarding Probability of Boys. They don't agree, either.

 

[Pielorinho]

Thanks for that link, Piratecat -- far from throwing oil on the fire, it shows how one could reach Merak's conclusion. I think he's reaching it incorrectly, given the wording we got and given his subsequent reasoning, but if the speaker could equally have said, "one of whom is a girl," then the odds of the second kid being male would indeed be 50/50. I'm assuming that if neither of the kids is male, that possibility is dropped from consideration.

Daniel

 

[MerakSpielman]

I see the problem we're having. We're essentially agreeing. Your web site shows this rather well.

Any random child has a 50-50 chance of being either gender.

I am assuming that the second child in any sequence will be a randomly selected child, and you are assuming that the child's sex will be predetermined.

So I'm saying that if a woman has two babies, each is equally likely to be a boy or a girl.

You're saying that in the population of women who have had 2 babies, those who have at least 1 boy are more likely to have 2 boys than to have a boy and a girl.

Now I understand what you were getting at - I remember this aspect of the sex-puzzles from math class.

For example, if you have a family of 3 children, all boys, the odds of the next child being a boy/girl are 50-50, but among existing families with 4 children, you're more likely to have 3 of one gender and 1 of the other.

 

[Pielorinho]

I think that's it, Merak. Basically, I solved the puzzle with the order the clauses were given to us; I assumed that we started off with two children and were narrowing down from there. Obviously the gender of one child doesn't affect the gender of the next child (although the article has some interesting social theory to the contrary, a puzzle like this can ignore such theory).

Ain't the Internet fun?
Daniel

 

[Pielorinho]

I am sad, however, that I'm not going to win fifty bucks.

Daniel

 

[MerakSpielman]

As soon as I saw the way you were figuring the odds there was no way I was going to bet. I'll take you up on your bet if you'll take me up on my coin-flipping bet.

I guess if we weren't both right we wouldn't have been able to argue for so long.

I suppose I need to get back to work now...

 

[Pielorinho]

You'll take me up on my bet for $50 if I take you up on your bet for any amount? Excellent!

Okay, I bet you fifty bucks than mine works the way I say, and I bet you a bright shiny nickel that yours works the way you say.

Daniel
who never lets a smartass opportunity pass him by