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Lul Thyme
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Quebec, Canada
Aug 2000
time: 05:16
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Well if if makes you feel good to think that its warped then be my guest.
but the fact is that if you know that there are two children in a household, and a boy answers the door (and we suppose the one who answers the door is random), then the chances are 1/3 that the other is a boy...
Nothing warped about it, its not about warping words.
If you go around your neighbourhood, check out houses with 2 kids, and count how many of them have at least a boy, 1/3 of those will have 2 boys.
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General Ludd
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Minion of the Dominion
Aug 2001
time: 05:16
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If you read what I said, I hadn't actually read the question properly and I thought it was a quesiton of the chances of giving birth to another boy and not a question of giving birth to two boys over two pregnancies.
There are four possible orders of giving birth in two pregnancies:
1. Boy, Girl
2. Boy, Boy
3. Girl, Girl
4. Girl, Boy
Now, if you are examining a family and don't know the order of the births one and four merge and it is a 1/3 chance of having two boys.
But if it is a question of a second child being born after there is already a boy, you remove three and four and it is a 1/2 chance.
That's why I called it warped odds - because it can imply that the chances of giving birth to a boy are lower if you have alreay had a boy. (which is what I originally thought the question was about)
EDIT:
 Actually, when you add the qualifier of "one of them is a boy" - as the original question did - that would give the same result, because it would cancel number three and merge one and four, leaving a chance of 1 in 2 - either a boy and a girl, or two boys.
EDIT again:
Of, I see. You can't actually merge Girl, boy and Boy, girl because you have to account for both. Only if you know the first born was a boy is it 1/2 that the next born child is also a boy.
but then again, that would also be true if you knew the second born was a boy.... because it's then a 50/50 quetstion of the first born
So it's only when you are uncertain of the order of birth that it's 1/3, because it adds a second hidden question of wether the boy was born first or second.
So, in effect, the qualifier of one being a boy doesn't actually mean anything.
EDIT yet again  : Actually, that should also apply to the first posibility before any qualifiers are added on, so there would be a 1/4 chance of having two boys, and the qualifier reduces it to 1/3 by knocking out the girl/girl possibility. So it does mean something. 
Last edited by General Ludd on 27-12-2004 at 01:19
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Lul Thyme
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Quebec, Canada
Aug 2000
time: 05:16
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Yes Krazyhorse.
But thats only part of the thing.
Even if I had the added statement that every family has at least 2 kids it makes no difference, though I know you understand by your first post.
Just to make it clear to everyone that this is not the important explanation. (which UR gave)
Imagine 2 families, one with 4 kids the other with 6 kids.
Average family size is 5, but if you ask the 10 kids randomly, 4/10 ull get 4, 6/10 ull get 6, for an average of 5.2....
Its funny how things that appear obvious are not always...
For example a batter in baseball can have a higher average in both half seasons than another batter, but a lower average for the whole season...
BTW a practical bet you can make with ppl that takes advantage of the second question of this thread.
You have 3 cards, on is both sides black, one is both sides red, last is one side red one side black.
You take a random card from a hat, say and look at one side.
Its red, say, so its either the red red or red\black, and he bets even money its red red since there are two choices.
Fair bet?
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Lul Thyme
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Quebec, Canada
Aug 2000
time: 05:16
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It has nothing to do with baseball...
You can have a higher average income per person for white than ppl in 2 countries, but in the two countries together blacks have higher average.
Or whatever example you want, meaning if something has higher average in two populations it might not have higher average in the pooled population.
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Lul Thyme
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Quebec, Canada
Aug 2000
time: 05:16
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BTW dauphin you should correct your link, it has a typo..
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Lul Thyme
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Quebec, Canada
Aug 2000
time: 05:16
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quote:
Originally posted by Snowflake
Wow that is a good trick. I guess it is more likely the card you picked is the one with both sides red. Since it is less likely you picked the R/B card and you happen to see the R side. |
Yes the odds are 2/3 thats its the double colored card and 1/3 that its the card with different colors...
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shawnmmcc
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OK, I get the apparent paradox - giggle, giggle - and we had lots of fun, too. You are pre-eliminating certain conditions, which I should have caught in your original description. I understand why so many mathematicians got it wrong, too. If you've been running plain vanilla multi-variant stats, you never have this kind of situation, in fact because so many experiments are double-blind, you go out of your way to prevent it. Thus many people who have run statistics for real world experiments will try to fit this into the paradigm of standard statistical studies, which it isn't. Yet it's just similiar enough to mislead someone who's been doing it.
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26-12-2004 18:53
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