Author Topic: LessWrongWiki: What the hell are they talking about?  (Read 18515 times)

Nephew Twiddleton

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Re: LessWrongWiki: What the hell are they talking about?
« Reply #90 on: September 03, 2013, 05:30:23 pm »
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.

When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?

Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.

The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.


This is reminding me of the time that my stats professor said he doesn't usually play the lottery because, statistically, there's no point, but when he feels like it, he'll go up and say loudly enough for the other numbers players to hear that he's playing 0000, just to piss them off. Each ball has 10% chance of coming up a 0, and on the off chance that 0000 does come up, he'll have been the only spag to play that number.

 :lulz: :lulz: :lulz:

That was my reaction, too. I like the idea of a mathematician trolling gamblers.
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Re: LessWrongWiki: What the hell are they talking about?
« Reply #91 on: September 03, 2013, 05:36:45 pm »
The conversation here is almost exactly like the conversation in my head when I was trying to figure out the problem. Still makes my head hurt.

My understanding is that the name Florida is meant to be misleading. It could be replaced with Susan, or anything. I think it's just important that we know some type of specific information about one of the girls, I think.

but I'm still missing something.

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Re: LessWrongWiki: What the hell are they talking about?
« Reply #92 on: September 03, 2013, 05:37:17 pm »


That leaves only 3 outcomes in the sample space: (girl, boy), (boy, girl), and (girl, girl).

I have to take issue with this, because as LG pointed out earlier there are 4 outcomes: (girl, boy), (boy, girl), (girl, girl) and (girl, girl). Just because (girl, girl) and (girl, girl) look identical doesn't mean you can discount one.

You could also look at it as a 25% chance for each (boy, girl) and (girl, boy) and a 50% chance of (girl, girl), though. But you can pretty safely dismiss the bloggers who are looking at it as somehow indicating that there is only a 1/3 chance of (girl, girl) because they clearly have no idea what they're talking about from the word go, so any further analysis from them is a waste of time.
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Re: LessWrongWiki: What the hell are they talking about?
« Reply #93 on: September 03, 2013, 05:41:35 pm »
The conversation here is almost exactly like the conversation in my head when I was trying to figure out the problem. Still makes my head hurt.

My understanding is that the name Florida is meant to be misleading. It could be replaced with Susan, or anything. I think it's just important that we know some type of specific information about one of the girls, I think.

but I'm still missing something.

It sounds like, from the excerpt that Rat posted, the original author of the question was using the name Florida to trigger some kind of discussion of the theoretical economics of the name; it doesn't appear to be a book about statistics, but a book about randomness, and so the question is not meant to be answered literally from a statistical perspective.
Im guessing it was January 2007, a meeting in Bethesda, we got a bag of bees and just started smashing them on the desk, Charles Wick said. It was very complicated.


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Re: LessWrongWiki: What the hell are they talking about?
« Reply #94 on: September 03, 2013, 05:49:14 pm »
Ok, I think I'm getting on board, but...
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.

When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?

Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.

The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.

So, if we real-timed this..

I happen to have a coin.  Before I flip it, what's the probability it will turn up heads twice?  25%.

I flip the coin once, and don't tell you what it was.  Before I flip the second one, what's the probability it will turn up heads twice?  25%.

I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice?  25%.

I turn over one of the coins.  It's heads.  What's the probability it will turn up heads twice?


...oh.


OH.

I turn over one of the coins.  It's heads.  What's the probability the other one is heads?  50%



And if I ask you what were the chances both of them would have come up heads... would you say 25%?

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Re: LessWrongWiki: What the hell are they talking about?
« Reply #95 on: September 03, 2013, 05:53:44 pm »
YOU GOT IT!

But the question asked isn't the one you answered. You answered the one I read (where we didn't know the gender of either kid at first). But yay for wrapping your head around a super useful concept for future things!

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Re: LessWrongWiki: What the hell are they talking about?
« Reply #96 on: September 03, 2013, 05:58:28 pm »
YOU GOT IT!

But the question asked isn't the one you answered. You answered the one I read (where we didn't know the gender of either kid at first). But yay for wrapping your head around a super useful concept for future things!

Wait, what?

Quote
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?

2 girls = two coin flips.

girl = heads

1 gender known = 1 flip known.

Probability of 2 girls = probability of two heads.

As per the above, 50%. 



What am I missing now?

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Re: LessWrongWiki: What the hell are they talking about?
« Reply #97 on: September 03, 2013, 06:00:00 pm »
Ok, I think I'm getting on board, but...
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.

When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?

Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.

The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.

So, if we real-timed this..

I happen to have a coin.  Before I flip it, what's the probability it will turn up heads twice?  25%.

I flip the coin once, and don't tell you what it was.  Before I flip the second one, what's the probability it will turn up heads twice?  25%.

I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice?  25%.

I turn over one of the coins.  It's heads.  What's the probability it will turn up heads twice?


...oh.


OH.

I turn over one of the coins.  It's heads.  What's the probability the other one is heads?  50%



And if I ask you what were the chances both of them would have come up heads... would you say 25%?

Yes.

The key is in the word "probability". Probability collapses into reality the moment a potential becomes an actual.
Im guessing it was January 2007, a meeting in Bethesda, we got a bag of bees and just started smashing them on the desk, Charles Wick said. It was very complicated.


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Re: LessWrongWiki: What the hell are they talking about?
« Reply #98 on: September 03, 2013, 06:00:17 pm »
As long as you're saying it's 50% either way, nothing.

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Re: LessWrongWiki: What the hell are they talking about?
« Reply #99 on: September 03, 2013, 06:02:27 pm »
YOU GOT IT!

But the question asked isn't the one you answered. You answered the one I read (where we didn't know the gender of either kid at first). But yay for wrapping your head around a super useful concept for future things!

No, he got it. Right here:

OH.

I turn over one of the coins.  It's heads.  What's the probability the other one is heads?  50%
Im guessing it was January 2007, a meeting in Bethesda, we got a bag of bees and just started smashing them on the desk, Charles Wick said. It was very complicated.


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Re: LessWrongWiki: What the hell are they talking about?
« Reply #100 on: September 03, 2013, 06:09:29 pm »
You could even look at it from an IRL POV:

"Hi, Betty!  It's me.  How's little Sheila doing?  That's great.  What?  You're pregnant again?  Great news!  Do you know if it's a girl or a boy?  Not yet?  Well, it could go either way, right?  fifty-fifty."


"Betty, it's me again!  How's baby Janice?  Wonderful news!  I know, two girls, isn't that something?  1 in 4 chance, like they say..."

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Re: LessWrongWiki: What the hell are they talking about?
« Reply #101 on: September 03, 2013, 06:16:38 pm »

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.

I know this is yesterday's post but I wanted to revisit it to point out that the name of the other girl isn't part of the question, so the fifth possibility you included there is invalid, as is designating one of the girls "Not Florida". Other than that you were on the right track in recognizing that there are two (girl, girl) possibilities; there are (girl, Florida) and (Florida, girl). The second girl, if she exists, could be named Florida or not be named Florida.
Im guessing it was January 2007, a meeting in Bethesda, we got a bag of bees and just started smashing them on the desk, Charles Wick said. It was very complicated.


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Re: LessWrongWiki: What the hell are they talking about?
« Reply #102 on: September 03, 2013, 06:17:19 pm »
You could even look at it from an IRL POV:

"Hi, Betty!  It's me.  How's little Sheila doing?  That's great.  What?  You're pregnant again?  Great news!  Do you know if it's a girl or a boy?  Not yet?  Well, it could go either way, right?  fifty-fifty."


"Betty, it's me again!  How's baby Janice?  Wonderful news!  I know, two girls, isn't that something?  1 in 4 chance, like they say..."

Yes, exactly.
Im guessing it was January 2007, a meeting in Bethesda, we got a bag of bees and just started smashing them on the desk, Charles Wick said. It was very complicated.


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Re: LessWrongWiki: What the hell are they talking about?
« Reply #103 on: September 03, 2013, 06:21:51 pm »
I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice?  25%.

I turn over one of the coins.  It's heads.  What's the probability it will turn up heads twice?


...oh.


OH.

I turn over one of the coins.  It's heads.  What's the probability the other one is heads?  50%

Now you know how Vegas makes money.
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Re: LessWrongWiki: What the hell are they talking about?
« Reply #104 on: September 03, 2013, 07:07:21 pm »
The conversation here is almost exactly like the conversation in my head when I was trying to figure out the problem. Still makes my head hurt.

My understanding is that the name Florida is meant to be misleading. It could be replaced with Susan, or anything. I think it's just important that we know some type of specific information about one of the girls, I think.

but I'm still missing something.

It sounds like, from the excerpt that Rat posted, the original author of the question was using the name Florida to trigger some kind of discussion of the theoretical economics of the name; it doesn't appear to be a book about statistics, but a book about randomness, and so the question is not meant to be answered literally from a statistical perspective.

Somehow this makes the problem even more interesting in some discordian koan way ;)
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