Super Duper Extra Hard Brainteaser

[mostsmooth]

i vote we wait for bruce

[gaming_mouse]

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Seems that way, but I can't quite wrap my head around it. If I take 1000 girls, 990 will be named Sarah - yet 495 will have a sister not named Sarah. How does that work?

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Who says they all have to have a sister not named sara?

You are looking at the wrong population. The population you want to look at is all 2 children families with one child named sara, not all the girls named sara.

[gaming_mouse]

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i vote we wait for bruce

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Patrick has rejected using Bruce as an arbitrator, though I am perfectly willing to do so.

[jason_t]

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Patrick has rejected using Bruce as an arbitrator, though I am perfectly willing to do so.

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Patrick: Please suggest an arbitrator.

[hoyaboy1]

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Seems that way, but I can't quite wrap my head around it. If I take 1000 girls, 990 will be named Sarah - yet 495 will have a sister not named Sarah. How does that work?

[/ QUOTE ]

Who says they all have to have a sister not named sara?

You are looking at the wrong population. The population you want to look at is all 2 children families with one child named sara, not all the girls named sara.

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Ok, that is a good point - my 1000 girls example is wrong. I have a followup in a second, but I figured I acknowledge this first.

Edit - How about this: we take 1000 girls from 2 child families (a small adjustment). 990 of them should be named Sarah, no? That only leaves 10 other girls to be sisters of half of them, which doesn't work.

So are we assuming that somehow Sarahs are really more prevelant in families with more or less than 2 kids so that this works out, or am I still missing something?

[gaming_mouse]

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Patrick has rejected using Bruce as an arbitrator, though I am perfectly willing to do so.

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Patrick: Please suggest an arbitrator.

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He's totally backing down. I'm a nice guy, though. I would let Patrick off the hook for $50 and Patrick changing his location for the next month to "Getting pwned by GM & jason_t".

[jason_t]

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He's totally backing down. I'm a nice guy, though. I would let Patrick off the hook for $50 and Patrick changing his location for the next month to "Getting pwned by GM & jason_t".

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[gaming_mouse]

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Edit - How about this: we take 1000 girls from 2 child families (a small adjustment). 990 of them should be named Sarah, no? That only leaves 10 other girls to be sisters of half of them, which doesn't work.

So are we assuming that somehow Sarahs are really more prevelant in families with more or less than 2 kids so that this works out, or am I still missing something?

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Given you parameters, you would just not be able to have that many 2 children homes containing Saras.

I think the way your trying to visualize may be misguided -- none of this stuff affects the probability calculation. Don't try to imagine the solution in this sense. Think of infinite population, so you don't have to deal with any of these issues.

If you really want to understand it intuitively, just try to understand the conditional probability theorem intuitivly (this is fairly easy), and then this will make sense.

[hoyaboy1]

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Edit - How about this: we take 1000 girls from 2 child families (a small adjustment). 990 of them should be named Sarah, no? That only leaves 10 other girls to be sisters of half of them, which doesn't work.

So are we assuming that somehow Sarahs are really more prevelant in families with more or less than 2 kids so that this works out, or am I still missing something?

[/ QUOTE ]

Given you parameters, you would just not be able to have that many 2 children homes containing Saras.

I think the way your trying to visualize may be misguided -- none of this stuff affects the probability calculation. Don't try to imagine the solution in this sense. Think of infinite population, so you don't have to deal with any of these issues.

If you really want to understand it intuitively, just try to understand the conditional probability theorem intuitivly (this is fairly easy), and then this will make sense.

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I think this is what I am getting at - it only works with an infinite population. If we are talking about earth, for example, 99% would change the answer a TON, as the odds of having a second girl would be waaaaaaaaaaay lower (of course, this whole thing would only work if people were killing off their second kid once they had a Sarah).

But, anyway, assuming we are talking about our planet, the answer is NOT the same for 1% and 99%.

[gaming_mouse]

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I think this is what I am getting at - it only works with an infinite population. If we are talking about earth, for example, 99% would change the answer a TON, as the odds of having a second girl would be waaaaaaaaaaay lower (of course, this whole thing would only work if people were killing off their second kid once they had a Sarah).

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No, no. It doesn't change the calculation at all. I wasn't suggesting that. It's just that you are making up these numbers, and then trying to imagine realistic situations (ie, population distributins like ours here on earth) where they occur.

But look, I can get around your objection by just having 1 or 2 two person families with a girl named sara. All the rest have 1 kid or 3+ kids.