I hate to keep posting but i keep getting ideas when it is too late to edit.
but anyways,
I think I see what was being shot for.
child a - girl child b - boy (1/3% contains a boy as the other child)
child a - girl child b - girl (1/3% has a girl as the other child)
child a - boy child b - girl (1/3% has a boy as the other child)
child a - boy child b - boy elimated because atleast one is a girl
but this seems like a combination problem and essentially choices 1 and 3 are the same and so one should be eliminated. if i say i have two marbles in a bag and one is red. does it really matter if i say “one marble is red and the other is blue” or “one marble is blue and the other is red?” in the end i have a red marble and a blue marble (or a blue marble and a red marble, whichever you prefer).
Look at this way: In 200 two children families; 50 families will have no boys, 100 families will have 1 boy, and 50 families will have 2 boys. Eliminate the 50 families with 2 boys because the family has at least 1 girl, of the remaining 150 families 100 of them have 1 boy and 1 girl and 50 of them have 2 girls giving a ratio of 2:1 for families where the other child is a boy.
How you find out that a family has at least 1 girl however is what determines whether the answer is 1/2 or 1/3
I think i know how to get the 66% that the other child is a male. take this scenario. you’re at a party and you meet a 13 boys and girls. 3 girls and boys greet you then my daughter then 3 more girls and boys. then i ask you to guess whether
my son greeted you first and then my daughter
my son greeted you first and then my son
my daughter greeted you first and then my daughter
my daughter greeted you first and then my son
option 2 is elimated because one of my children is a girl. In this scenario, given this information, the odds that the other child was a boy is 2/3. I’m not sure how that affects your odds of getting my question right. that still seems to be a 1/3 chance. Maybe if you assume the other child is a boy your odds of getting my question will increase to 2/3 also?
What it boils down to is this. If you can say only, “There are two children and one is a boy,” the odds are 2/3. If you can say, “There are two children and this one is a boy,” the odds are 1/2. The mere this (or that) is the necessary and sufficient distinction.
Why? Saying “this” child doesn’t change the fact that the other child is unknown and would have to come from the conditional probability (2/3 boy, 1/3 girl).
Whilst it is a necessary condition to have a boy in order to say either “one is a boy” or “this one is a boy” it isn’t a sufficient condition, since a family with a boy and a girl one could equally say “one is a girl” or “this one is a girl”. The answer in both versions is 1/2, unless there is a constraint such that only boys are mentioned when there is 1 of each - which seems an unreasonable assumption to make.
In a 2 child family the existence of (at least) one boy is not a sufficient condition for being told “(at least) one is a boy”, as is apparent in the case where the family is made up of a boy and a girl where the statement “(at least) one is a girl” could equally be made.
In other words being told “(at least) one is a boy” is not guaranteed by the existence of (at least) one boy in the family - which is the definition of a sufficient condition.
Actually it does make a difference, and understanding that fact is fundamental to getting the correct answer.
If you learn that the family has a girl in such a way that the question would be asked, “What are the chances that one of them is a boy?”, the answer is 2/3.
If you learn that the family has a girl in such a way that the question would be asked, “What are the chances that the other one is a boy?”, the answer is 1/2.
The reason the answer to the first question is 2/3 is because there are two different combinations that contain a boy. As soon as you specify one child in any way, you have eliminated one of those combinations.
If they don’t, they’re either withholding the information implied by the basic conditions, in which case they’re irrelevant, or they’re lying, which brings us into a whole new class of puzzles.
Well the basic conditions are a bit up in the air. I’m not suggesting we consider people who lie to a direct question about their kids. There was mention upthread about meeting someone at a party. In that case we would assume that a person who chooses to mention having a son really does have one, but we not assume that every person who had a son would necessarily announce that, nor would we assume that every person who did not choose to mention a son did not in fact have one.
It’s not clear what information is implied by the basic conditions, anyway. Is the basic condition that the person picks a child at random, and then says “I have a boy” or “I have a girl” accordingly? Is the basic condition that the person says “I have a boy” if that is a true statement, or says nothing if it isn’t true? Is the basic condition that the person takes one true statement at random from the set of statements “I have a boy” and “I have a girl”? Different basic conditions will lead to different probabilities.
Not at all. The statements “(at least) one is a boy” and “(at least) one is a girl” are both equally truthful and likely to be said of a family that has one boy and one girl.
That’s why the answer to the puzzle “There are two children and one is a boy” is 1/2 and not 2/3, as there’s only a 50% chance this statement will be made about a BG/GB family.
This is what happens when a man is too damn arrogant to ever admit that he screwed up. First off, he botched the answer (switch = 2/3 chance of winning, stay = 1/3 chance of winning, switch is better) either because he didn’t read it correctly, or thought it was beneath him and rushed off his response, I dunno. Then, when called on it, he pulled out a ham-handed “Of COURSE I knew that; I was talking about a REAL WORLD situation, and Monsieur Hall would NEVER be so STUPID as to blah blah blah” CYA which only dug him in deeper.
If he really thought the original question was too easy or beneath his dignity or whatever, what he should have done is answer it and then give his follow-up question. He’s done this quite a few times; I don’t understand why it would be such a problem here. Given that he rips into Marilyn Von Savant pretty hard for no clear reason, I have to believe that his whole motive was some petty vendetta against someone else with a Q&A column, and he took what was supposedly an easy shot which turned into anything but.
