LessWrongWiki: What the hell are they talking about?

[Nephew Twiddleton]

The Girl Named Florida problem is usually preceded by an easier problem that goes as follows:

Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?

Now for the Girl Named Florida problem:

Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?

Bolded the part I read past over and over again.

I'm still missing it. I thought that at least one girl was a given. The probability of the gender of the second child is independent of that. Are we talking about the at least one girl problem or the girl named Florida problem?

Both problems appear to be the same question. They are identical. The name of the "at least one girl" is irrelevant. The only difference between the two questions are the two words "named Florida".

Fair. I'm still not getting it though. Family has two kids. At least one of them is a girl. That means that the options are:
1 girl, 1 boy
2 girls

We already know that the family has one girl, so the probability is the gender of the second child only, no? I'm missing Gogira's revelation entirely. Since the one child being a girl is part of the priors, that brings the probability of to girls up to 50%, not 25% or 60%?

[Bebek Sincap Ratatosk]

The Girl Named Florida problem is usually preceded by an easier problem that goes as follows:

Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?

Now for the Girl Named Florida problem:

Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?

Bolded the part I read past over and over again.

I'm still missing it. I thought that at least one girl was a given. The probability of the gender of the second child is independent of that. Are we talking about the at least one girl problem or the girl named Florida problem?

Both problems appear to be the same question. They are identical. The name of the "at least one girl" is irrelevant. The only difference between the two questions are the two words "named Florida".

Thanks Nigel, I couldn't figure out any difference between the two questions when I read this thread yesterday and my brain started leaking out of my ear.

[Q. G. Pennyworth]

Yeah, I screwed up and thought that the

The Girl Named Florida problem is usually preceded by an easier problem that goes as follows:

Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?

Now for the Girl Named Florida problem:

Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?

Bolded the part I read past over and over again.

I'm still missing it. I thought that at least one girl was a given. The probability of the gender of the second child is independent of that. Are we talking about the at least one girl problem or the girl named Florida problem?

Both problems appear to be the same question. They are identical. The name of the "at least one girl" is irrelevant. The only difference between the two questions are the two words "named Florida".

Fair. I'm still not getting it though. Family has two kids. At least one of them is a girl. That means that the options are:
1 girl, 1 boy
2 girls

We already know that the family has one girl, so the probability is the gender of the second child only, no? I'm missing Gogira's revelation entirely. Since the one child being a girl is part of the priors, that brings the probability of to girls up to 50%, not 25% or 60%?

All of them are 50% because there's no difference between the two sentences as far as the genders are concerned. I screwed up and read the first sentence without the "one of them is a girl" part, which would make it "one family has two kids and you have no information about either gender." Because I am a moron.

[Bebek Sincap Ratatosk]

Hrmmm... so I googled this and there seems to be all sorts of debate.

So far I am most swayed by the 50% argument. However, I did find an argument for WHY the name Florida would change the probabilities. Florida is an uncommon name. Therefore there is a higher probability of a girl being named Florida if there are two girls, rather that one.

That is Boy/Girl(Florida) or Girl(Florida)/Boy are supposedly less likely than Girl/Girl (Florida) or Girl(Florida)/Girl.

I don't know if I agree with that, but it at least provides some rationale for the additional piece of data.

ETA:
Another argument:

For the first question we have the options:
Boy/Girl, Girl/Girl, Girl/Boy

So 1/3 chance that the second child is a girl.

For the second question we have the following options:
Boy/Girl named Florida, Girl Named Florida/Boy, Girl/Girl Named Florida, Girl Named Florida/Girl.

So 2/4 (1/2) chance that the second child is a girl.

Though that seems kinda shady to me since Girl/Girl is just being counted twice.

[Mesozoic Mister Nigel]

Hrmmm... so I googled this and there seems to be all sorts of debate.

So far I am most swayed by the 50% argument. However, I did find an argument for WHY the name Florida would change the probabilities. Florida is an uncommon name. Therefore there is a higher probability of a girl being named Florida if there are two girls, rather that one.

That is Boy/Girl(Florida) or Girl(Florida)/Boy are supposedly less likely than Girl/Girl (Florida) or Girl(Florida)/Girl.

I don't know if I agree with that, but it at least provides some rationale for the additional piece of data.

ETA:
Another argument:

For the first question we have the options:
Boy/Girl, Girl/Girl, Girl/Boy

So 1/3 chance that the second child is a girl.

For the second question we have the following options:
Boy/Girl named Florida, Girl Named Florida/Boy, Girl/Girl Named Florida, Girl Named Florida/Girl.

So 2/4 (1/2) chance that the second child is a girl.

Though that seems kinda shady to me since Girl/Girl is just being counted twice.

That logic is erroneous because the fact that the girl is named Florida is given. The commonness or uncommonness of the name has zero bearing.

[Nephew Twiddleton]

Hrmmm... so I googled this and there seems to be all sorts of debate.

So far I am most swayed by the 50% argument. However, I did find an argument for WHY the name Florida would change the probabilities. Florida is an uncommon name. Therefore there is a higher probability of a girl being named Florida if there are two girls, rather that one.

That is Boy/Girl(Florida) or Girl(Florida)/Boy are supposedly less likely than Girl/Girl (Florida) or Girl(Florida)/Girl.

I don't know if I agree with that, but it at least provides some rationale for the additional piece of data.

ETA:
Another argument:

For the first question we have the options:
Boy/Girl, Girl/Girl, Girl/Boy

So 1/3 chance that the second child is a girl.

For the second question we have the following options:
Boy/Girl named Florida, Girl Named Florida/Boy, Girl/Girl Named Florida, Girl Named Florida/Girl.

So 2/4 (1/2) chance that the second child is a girl.

Though that seems kinda shady to me since Girl/Girl is just being counted twice.

So is Girl/Boy in the 1/3 chance. The position of the girl has no bearing. They're not asking that. Girl/Boy is the same as Boy/Girl.

[Nephew Twiddleton]

Yeah, I screwed up and thought that the

The Girl Named Florida problem is usually preceded by an easier problem that goes as follows:

Suppose you know that a family with two children has at least one girl. What is the probability that this family has two girls?

Now for the Girl Named Florida problem:

Suppose you know that a family with two children has at least one girl named Florida. What is the probability that this family has two girls?

Bolded the part I read past over and over again.

I'm still missing it. I thought that at least one girl was a given. The probability of the gender of the second child is independent of that. Are we talking about the at least one girl problem or the girl named Florida problem?

Both problems appear to be the same question. They are identical. The name of the "at least one girl" is irrelevant. The only difference between the two questions are the two words "named Florida".

Fair. I'm still not getting it though. Family has two kids. At least one of them is a girl. That means that the options are:
1 girl, 1 boy
2 girls

We already know that the family has one girl, so the probability is the gender of the second child only, no? I'm missing Gogira's revelation entirely. Since the one child being a girl is part of the priors, that brings the probability of to girls up to 50%, not 25% or 60%?

All of them are 50% because there's no difference between the two sentences as far as the genders are concerned. I screwed up and read the first sentence without the "one of them is a girl" part, which would make it "one family has two kids and you have no information about either gender." Because I am a moron.

Gotcha. I was confused as to where you were coming from and thought that I was wrong about the 50%

[LMNO]

Reframe: Coin flips.

Round 1:
Heads 1/2
Tails 1/2

Round 2
Heads Heads 1/4
Heads Tails 1/4
Tails Heads 1/4
Tails Tails 1/4

But in this case, the order doesn't matter.

So,
Heads Heads 1/4
[Hails Teads] 2/4
Tails Tails 1/4


So the chance of two girls is 25%?

... Did I totally get a different answer here?  Goddammit.

[Bebek Sincap Ratatosk]

Hrmmm... so I googled this and there seems to be all sorts of debate.

So far I am most swayed by the 50% argument. However, I did find an argument for WHY the name Florida would change the probabilities. Florida is an uncommon name. Therefore there is a higher probability of a girl being named Florida if there are two girls, rather that one.

That is Boy/Girl(Florida) or Girl(Florida)/Boy are supposedly less likely than Girl/Girl (Florida) or Girl(Florida)/Girl.

I don't know if I agree with that, but it at least provides some rationale for the additional piece of data.

ETA:
Another argument:

For the first question we have the options:
Boy/Girl, Girl/Girl, Girl/Boy

So 1/3 chance that the second child is a girl.

For the second question we have the following options:
Boy/Girl named Florida, Girl Named Florida/Boy, Girl/Girl Named Florida, Girl Named Florida/Girl.

So 2/4 (1/2) chance that the second child is a girl.

Though that seems kinda shady to me since Girl/Girl is just being counted twice.

That logic is erroneous because the fact that the girl is named Florida is given. The commonness or uncommonness of the name has zero bearing.

That's what I thought as well, however it seems to be a popular argument on the many blogs where this problem is discussed. In fact at this site: http://bblais.blogspot.co.uk/2010/01/there-once-was-girl-named-florida-aka.html Someone actually wrote a simulation and a formal analysis on the point.

I don't know enough to say that I agree, only that it seems pretty damn weird 

[Mesozoic Mister Nigel]

Both questions, as they are worded, are "what is the probability that the other child is a girl?"

[Mesozoic Mister Nigel]

Hrmmm... so I googled this and there seems to be all sorts of debate.

So far I am most swayed by the 50% argument. However, I did find an argument for WHY the name Florida would change the probabilities. Florida is an uncommon name. Therefore there is a higher probability of a girl being named Florida if there are two girls, rather that one.

That is Boy/Girl(Florida) or Girl(Florida)/Boy are supposedly less likely than Girl/Girl (Florida) or Girl(Florida)/Girl.

I don't know if I agree with that, but it at least provides some rationale for the additional piece of data.

ETA:
Another argument:

For the first question we have the options:
Boy/Girl, Girl/Girl, Girl/Boy

So 1/3 chance that the second child is a girl.

For the second question we have the following options:
Boy/Girl named Florida, Girl Named Florida/Boy, Girl/Girl Named Florida, Girl Named Florida/Girl.

So 2/4 (1/2) chance that the second child is a girl.

Though that seems kinda shady to me since Girl/Girl is just being counted twice.

That logic is erroneous because the fact that the girl is named Florida is given. The commonness or uncommonness of the name has zero bearing.

That's what I thought as well, however it seems to be a popular argument on the many blogs where this problem is discussed. In fact at this site: http://bblais.blogspot.co.uk/2010/01/there-once-was-girl-named-florida-aka.html Someone actually wrote a simulation and a formal analysis on the point.

I don't know enough to say that I agree, only that it seems pretty damn weird 

It may be a common argument, but it's a stupid one because he is answering a different question.

[Q. G. Pennyworth]

Reframe: Coin flips.

Round 1:
Heads 1/2
Tails 1/2

Round 2
Heads Heads 1/4
Heads Tails 1/4
Tails Heads 1/4
Tails Tails 1/4

But in this case, the order doesn't matter.

So,
Heads Heads 1/4
[Hails Teads] 2/4
Tails Tails 1/4


So the chance of two girls is 25%?

... Did I totally get a different answer here?  Goddammit.

You got the right math for the wrong problem, I missed a key phrase in the question and I think I've hopelessly confused the thread 

[Mesozoic Mister Nigel]

Let me put it this way: Once you have a given, the probability of the given is 100%. It is no longer a factor in the calculation for the probability of the not-given.

[LMNO]

Both questions, as they are worded, are "what is the probability that the other child is a girl?"

Yes, and when you're given the information that one of them is a girl, the question moves from "what are the chances that a child is born a girl," and becomes "What are the chances that two children are both born girls?" 

Or, in other words, you're asked about two coin flips, not just one.

If I flip a coin four times, the sequence of flips has 1/16 chance of happening.  But if I ask what the chances of any given flip, then it's 1/2.

And if I ask the odds of the total amount of heads v tails, that's another probability entirely.

[Mesozoic Mister Nigel]

For the record, that is the kind of question that is given in statistics classes to train students to disregard extraneous data. As this thread illustrates perfectly, one of the challenges in statistics is to answer the question that is actually being posed and not the question that you think is being posed.