Maths Problem

[Solly]

Yes, assuming that the woman has two children and that at least one is a boy, the odds of her having two boys is 1/3.

Glad this one met less resistance!

[Lul Thyme]

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.

[General Ludd]

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.

[Lul Thyme]

Well if you argument convinces you then great!
Now we all agree

There are actually many statements which sound peculiar...

This one even suprised me :
Suppose in a population the average number of kids per family is 3.
If I go around the same population asking random kids how many kids there are in their family, what should I expect to get as average answer?

(By average I mean arithmetic mean...)

[chequita guevara]

Cecil Adams explained this years ago, but I never understood it 'till now. Thanks guys.

[KrazyHorse]

Originally posted by Lul Thyme
Well if you argument convinces you then great!
Now we all agree

There are actually many statements which sound peculiar...

This one even suprised me :
Suppose in a population the average number of kids per family is 3.
If I go around the same population asking random kids how many kids there are in their family, what should I expect to get as average answer?

(By average I mean arithmetic mean...)

Something larger than 3.

[General Ludd]

Originally posted by Lul Thyme
Well if you argument convinces you then great!
Now we all agree

We agreed before that post aswell. I just hadn't bothered with problem before. And it's still a tricky word game that can leave people with a false impression if they don't think through the problem to it's fullest extent.

[reds4ever]

Originally posted by Lul Thyme
Well if you argument convinces you then great!
Now we all agree

There are actually many statements which sound peculiar...

This one even suprised me :
Suppose in a population the average number of kids per family is 3.
If I go around the same population asking random kids how many kids there are in their family, what should I expect to get as average answer?

(By average I mean arithmetic mean...)

Less than 3, you could be asking the first (and so far only) born of a family.

[Snowflake]

But if there are a lot of families with only one kid so far there must be other families with more than three kids currently to make the average number of kids per family 3. In other words I don't see why the answer to the question isn't 3.

[Snowflake]

Unless the first statement should be understood differently. If the first statment means the average total kids per family will have is three, in stead of the average current kids per family is three, then you are right.

[Urban Ranger]

Something bigger than 3.

If you go around asking random kids, there's a bigger chance of running into kids coming from big families than kids from small families.

[Snowflake]

Hmmm that's true. If there are only two families in the population and one family have five kids and one have one kid. The average per family is three. But if you ask all kids, then you'd get answers like 5,5,5,5,5,1. And the answer is obviously large than 3. Very good UR.

[KrazyHorse]

Guys, the answer to that question is obvious. Assuming that the population of orphans is small enough to be ignored or that they are instructed to answer "Don't Know" or something (and are thus removed from consideration) then when you ask the question of kids you can never get the answer "0". In other words there are adults without children but no children without adults.

[KrazyHorse]

Do an extreme example. For the sake of argument there are no orphans in Society X. There are 1000 married couples in this society. 500 of them are rabbits and have 6 kids each. 500 of them hate children and have 0 kids each. The arithmetic mean of kids/household is (6*500 + 0*500)/1000 = 3

If you ask the kids though, every kid will answer "6", and the arithmetic mean you get is 6.

You can't find out how many childless households there are by asking children. These childless households are actually removed from consideration by using this survey method.

[KrazyHorse]

It's like calling people up to ask them if they have a telephone. Everybody who answers the survey will say "yes"...