Probability?

[Micahle]

B+B
B+G
G+G

Those are the options - Doubling up B+G/G+B isn't relevant because the question isn't asking for the order of birth.

If you already have 1 boy, then there are only 2 options left - B+B and B+G. The chance of having B+B is therefore 50%.

That's my take on it anyway Is there an actual answer?

[Vexo]

Vexo - you didn't answer Weo's question about the grammar of the question you posed? Is that exactly accurate? If it is, it's badly flawed.

He went on to assume the correct form of it and I can't see where it's flawed, so, yeah, don't see how I can answer it.

[Vexo]

If you already have 1 boy, then there are only 2 options left - B+B and B+G. The chance of having B+B is therefore 50%.

You don't already have one boy... you know that one of them is a boy. Ergo you have to factor in the chance that both the first and the second child may end up being a girl.

The hard fractions are, 1/2 chance that you get BG (GB), 1/4 chance you get BB and 1/4 chance you get GG.

And there is an answer from a probability theory perspective.

[Micahle]

You don't already have one boy... you know that one of them is a boy.

I'm sorry.. what? You don't have a boy, but you do. That doesn't make sense.

So... I've got two kids...one is a boy, born on a Tuesday. What is the probability that I've got two boys?

How can you factor in having 2 girls, when there are only 2 kids and one is already a boy?

I've got = Already has.

[Creac]

Double use of the ellipsis is far from clear.

http://en.wikipedia.org/wiki/Ellipsis

If that's really how it was phrased, it's badly flawed regardless of Weo successfully determining the intended meaning.

[Kofn]

The cause for confusion is in the implicit assumption of a birth order.

If I have two kids, there are 4 equally likely outcomes:
- boy then boy
- boy then girl
- girl then boy
- girl then girl

Each of which has a 25% chance.

If I give the information "one of my kids is a boy", the only possible outcome that you can rule out is the last one (two girls).

That leaves three equally likely options, only one of which includes a second boy. 1 / 3 = 33%.

If the question was stated with the phrase "my oldest kid is a boy", then you can remove the last two options (GG and GB), which leaves you two equally likely outcomes, only one of which includes a second boy. 1 / 2 = 50%.

The birth order is important, whether you like it or not

The "born on the Tuesday" thing will similarly affect the probabilities.

These concepts are hard to understand intuitively, and you often need to write down all the possibilities before it makes sense (or at least I do!).

[Kofn]

For the people that still don't believe, answer this question:

I have two kids, what is the probability that both are boys?

[varutia]

For the people that still don't believe, answer this question:

I have two kids, what is the probability that both are boys?

Your assumption is incorrect, you have two kids, you get two chance of having it. One of them is taken up by a boy already. So you have only one chance of having or had another kids, in this one chance, the probably is 50% of having a girl or a boy.

Your listing of case are not correct all, see following, following two equation covered birth order question and you see does not matter which option you pick, you end up with 50/50.

G/B + B
B + G/B

G/B + B == B + G/B

The two equation are exactly same thing, birth order had zero affect on the unknown kid being a boy or girl or not.

[Vexo]

I've got = Already has.

I've got two kids. You're answering the question "My first-born child was a boy, what is the probability I have two sons?", which is not being asked. Both kids have already been born, but you don't know the order. Therefore, in calculating the probablity that both are boys, you cannot ignore the "risk" that your first-born was a girl OR that your second-born
was born with a vagina.

[Vexo]

Double use of the ellipsis is far from clear.

http://en.wikipedia.org/wiki/Ellipsis

If that's really how it was phrased, it's badly flawed regardless of Weo successfully determining the intended meaning.

Are you kidding me?

I've got two kids. One is a boy, born on a Tuesday. What is the probability that I've got two boys?

Happy? I don't see the sligthest bit of difference, but /shrugs

[Vexo]

For the people that still don't believe, answer this question:

I have two kids, what is the probability that both are boys?

Your assumption is incorrect, you have two kids, you get two chance of having it. One of them is taken up by a boy already. So you have only one chance of having or had another kids, in this one chance, the probably is 50% of having a girl or a boy.

Your listing of case are not correct all, see following, following two equation covered birth order question and you see does not matter which option you pick, you end up with 50/50.

G/B + B
B + G/B

G/B + B != B + G/B
The two equation are exactly same thing, birth order had zero affect on the unknown kid being a boy or girl or not.

As explained above, since you do not know that the boy in question was born first or last, GB and BG are two seperate "fail" outcomes, but they are NOT excluded, since both contain the only given you've required (one B), unlike GG which cannot factor in.

[Creac]

No, Vexo, not kidding. Remember, I'm the one you thanked for being the pedant I claim to be

And, yes, there's quite a difference.

[Micahle]

I've got = Already has.

I've got two kids. You're answering the question "My first-born child was a boy, what is the probability I have two sons?", which is not being asked. Both kids have already been born, but you don't know the order. Therefore, in calculating the probablity that both are boys, you cannot ignore the "risk" that your first-born was a girl OR that your second-born
was born with a vagina.

No, I wasn't answeing that question at all :p I was responding to your comment of "You don't already have one boy... you know that one of them is a boy.". Go read up, that's exactly what you said and I dunno if you maybe need to word it better but you're saying "I don't have a boy, but I do have a boy" Which is just nonsense.

[Vexo]

I've got = Already has.

I've got two kids. You're answering the question "My first-born child was a boy, what is the probability I have two sons?", which is not being asked. Both kids have already been born, but you don't know the order. Therefore, in calculating the probablity that both are boys, you cannot ignore the "risk" that your first-born was a girl OR that your second-born
was born with a vagina.

No, I wasn't answeing that question at all :p I was responding to your comment of "You don't already have one boy... you know that one of them is a boy.". Go read up, that's exactly what you said and I dunno if you maybe need to word it better but you're saying "I don't have a boy, but I do have a boy" Which is just nonsense.

Pfth, I was in a rush, explained it in the new posts. Maybe read it like this "You don't already have ONE boy, Baby Jesus, born on June 3rd 0 B.C.... you know that one of them is a boy.". I.e. both kids are already born, one of them is a boy... you're trying to answer what the probability is that both are boys.

Oh no, a massive amount of ellipsis! Do I have ellipsica? Here's (I think, just looked it up quickly) the exact way the question was posed:

I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?

[Vexo]

And, yes, there's quite a difference.

Which?

[Chunk]

50%

[Creac]

There's quite a difference between an ambiguous mish-mash of words and punctuation and something that uses correct syntax.

[Vexo]

There's quite a difference between an ambiguous mish-mash of words and punctuation and something that uses correct syntax.

So... (pause in speech) what I'm getting from you... (pause in speech) is that there's no distinct reason the question should be flawed to a degree of not being understandable, to any higher degree than most anything else posted on fora across the interwebs... (trailing off into silence)

Thank you for the clarification!

[Chunk]

50%

[Hiroki]

13/27

[Creac]

No, Vexo. You're not getting that from me. You're imposing your own view in order to justify your lack of syntax. That's all

[Vexo]

Answer is 13/27. Nice try at sabotage Ailsha :p Fortunately you failed!

Here's a decent explanation of the correct answer:

http://www.maa.org/devlin/devlin_04_10.html

Hopefully his credentials will help convince you, if you read it :p They're not half bad.

And he can probably use proper grammar, so you won't have that to hide behind, Creac :p

No, Vexo. You're not getting that from me. You're imposing your own view in order to justify your lack of syntax. That's all

Cows live in houses made out of grass.

I just contributed an equal amount to what I said previously as what you just said!

[Kofn]

Interesting. When you raised the relevance of Tuesday I realized it would change the probability, but didn't actually do the work and am now surprised it shifted it so much.

[Chunk]

50%

[Vexo]

Interesting. When you raised the relevance of Tuesday I realized it would change the probability, but didn't actually do the work and am now surprised it shifted it so much.

I find it curious, that the more determined you make it, the closer to 50% you get.