LessWrongWiki: What the hell are they talking about?

[Lord Cataplanga]

Even if the innovators are spitting out good stuff as often as they can, innovators don't tend to stay in one place.

Speaking of this, have you tried picking a few innovators you like and see where they went?
Many of lesswrong's top contributors have their own blogs, for example. Check their user pages.

I, for one, enjoy reading Gwern's site, Katja Grace's blog and Yvain's blog.

[McGrupp]

The way I understand it, this is the solution (though the second one still seems weird to me)

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

The possiblities are:

Boy-Girl
Girl-Boy
Girl-Girl

So the probability is 1 in 3.


Say you know a family has two children, and further that at least one of them is a girl named Florida. What is the probability that they have two girls?

Here we have:

Boy-Girl (Florida)
Girl (Florida)-Boy
Girl (Not Florida)-Girl (Florida)
Girl (Florida)-Girl (Not Florida)
Girl (Florida)-Girl (Florida)

Here we get 3/5 which is a  60 percent chance. Although they seem to take out the Florida Florida scenario (which kinda feels like cheating) and get a 50 percent chance. This still feels odd.

[LMNO]

That's the Monty Hall problem. It's also covered in the sequences.

[McGrupp]

That's the Monty Hall problem. It's also covered in the sequences.

Yes. That's another good one. I like hearing the stories of when Marilyn vos Savant answered the Monty Hall problem in her column and had hundreds of PhD's in statistics and engineering write in to tell her she was wrong. Funny stuff and also another really good example of where intuition can fall short.

[Q. G. Pennyworth]

The way I understand it, this is the solution (though the second one still seems weird to me)

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

The possiblities are:

Boy-Girl
Girl-Boy
Girl-Girl

So the probability is 1 in 3.


Say you know a family has two children, and further that at least one of them is a girl named Florida. What is the probability that they have two girls?

Here we have:

Boy-Girl (Florida)
Girl (Florida)-Boy
Girl (Not Florida)-Girl (Florida)
Girl (Florida)-Girl (Not Florida)
Girl (Florida)-Girl (Florida)

Here we get 3/5 which is a  60 percent chance. Although they seem to take out the Florida Florida scenario (which kinda feels like cheating) and get a 50 percent chance. This still feels odd.

It's not 1 in 3, it's 1 in 4. Just because you don't care about the birth order doesn't mean you get to collapse two potential outcomes into one.

[The Good Reverend Roger]

As a relative newcomer to PD.com I will say it can be a little intimidating to post. They always warn you that with discordians you won't be the weirdest person in the room but no one ever points out that you won't be the smartest person in the room.

Or how horrible the notion of being the smartest guy in the room can be.

[Nephew Twiddleton]

The way I understand it, this is the solution (though the second one still seems weird to me)

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

The possiblities are:

Boy-Girl
Girl-Boy
Girl-Girl

So the probability is 1 in 3.


Say you know a family has two children, and further that at least one of them is a girl named Florida. What is the probability that they have two girls?

Here we have:

Boy-Girl (Florida)
Girl (Florida)-Boy
Girl (Not Florida)-Girl (Florida)
Girl (Florida)-Girl (Not Florida)
Girl (Florida)-Girl (Florida)

Here we get 3/5 which is a  60 percent chance. Although they seem to take out the Florida Florida scenario (which kinda feels like cheating) and get a 50 percent chance. This still feels odd.

It's not 1 in 3, it's 1 in 4. Just because you don't care about the birth order doesn't mean you get to collapse two potential outcomes into one.

Yeah, it seems that the birth order is an irrelevant factor. You want to know the odds of one kid being something, not a specific kid.

But even then, gender is determined by sperm, and the likelihood of one particular gendered sperm out of millions to get to fertilize the egg makes the math a bit unwieldy. I get that it's mostly a coin toss, but that's only because out of millions of sperm cells, the lottery winner can't be predicted on just that. What I mean is you have to factor in the amount of sperm that even get to the egg. Not all of them get there, and the gender distribution of those isn't necessarily 50/50. Or am I overthinking this?

[LMNO]

You're over thinking this, in that the question is a hypothetical.

However, this is a great example of Bayes, in that you use the above probabilities until you encounter SPECIFIC FACTS about the genetic makeup if the parents, at which time you add them to your priors and then slide the probability up or down. Although, given what we've just covered, the sliding would most likely be in the tenths of a percent rather than anything significant.

[Nephew Twiddleton]

You're over thinking this, in that the question is a hypothetical.

However, this is a great example of Bayes, in that you use the above probabilities until you encounter SPECIFIC FACTS about the genetic makeup if the parents, at which time you add them to your priors and then slide the probability up or down. Although, given what we've just covered, the sliding would most likely be in the tenths of a percent rather than anything significant.

So, I'm thinking about this in a Bayesian way, but for an irrelevant example, yes?

[Mesozoic Mister Nigel]

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?

How are the probabilities for these two scenarios different? Is it a trick question? All it's asking is what the probability of the other child being a girl is in both cases.

[Q. G. Pennyworth]

...



I have been reading that wrong this entire time.




<appropriate "I'm an idiot" emote here>

[Nephew Twiddleton]

...



I have been reading that wrong this entire time.




<appropriate "I'm an idiot" emote here>

How so? It still seems like probability is birth order, which is irrelevant, unless I'm missing something too.

[Q. G. Pennyworth]

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.

[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?

[Mesozoic Mister Nigel]

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".