Re: Super Duper Extra Hard Brainteaser
 

i'm guessin 201/40000

Re: Super Duper Extra Hard Brainteaser
 

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i'm guessin 201/40000

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I wasn't really looking for an answer, and haven't worked it out. My point to Patrick was that is is quickly obvious that it is not 3/4, and thus the information about the girl is relevant, be it her preference for dolls, or her name.

Re: Super Duper Extra Hard Brainteaser
 

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I'll open with a well know semi-easy one:

You know that a woman has exactly 2 children. You ask her if she has at least one girl, and she says yes. What's the probability that she has two girls?

Answer in white:

<font color="white"> 1/3 </font>

Now, suppose that 1% of all girls are named Sarah, and that if a mother had two girls that the mother would not name both of them Sarah

You know a woman has exactly 2 children, you ask her if she has a girl named Sarah, she says yes.

What are the chances she has two girls?

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the answer isn't 1/3. we're drawing from 99% of the sample of girls, but 100% of the sample of boys. knowing that the second girl is NOT a sarah means that 1% of girls are unavailable for us to grab.

so say we have 99 girls and 100 boys, and we want to know the probability, given that one is a girl named sarah, that the other is a girl.

overall we can have

G, B
B, G
G, G

given that we have at least one girl. there are 100 ways to choose the boy in case 1, 100 ways to choose the boy in case 2, and 99 ways to choose the girl in case 3. so, I get 99/300.

initially it looks like conditional probability reduces this problem to the first one, but the "sarah stipulation" controls the sampling of the SECOND girl, not the sarah that we know to exist.

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that sounded good, but then you got an answer that no one has gotten yet

Re: Super Duper Extra Hard Brainteaser
 

what can I say, I'm a rebel.

Re: Super Duper Extra Hard Brainteaser
 

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i'm guessin 201/40000

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I wasn't really looking for an answer, and haven't worked it out. My point to Patrick was that is is quickly obvious that it is not 3/4, and thus the information about the girl is relevant, be it her preference for dolls, or her name.

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oh, yes i agree

Re: Super Duper Extra Hard Brainteaser
 

How are BG and GB different?

Re: Super Duper Extra Hard Brainteaser
 

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How are BG and GB different?

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So you think 2 boys, 2 girls and 1 of each are all equally likely?

Re: Super Duper Extra Hard Brainteaser
 

there are 4 ways a woman can have 2 kids
bb
bg
gb
gg

Re: Super Duper Extra Hard Brainteaser
 

Don't think of them as combinations of items from a group... think of them as a sequence of independent events.

Re: Super Duper Extra Hard Brainteaser
 

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How are BG and GB different?

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If it makes you feel better, we can just say that there's a 50% chance of having exactly one boy and one girl and 25% of having either two boys or two girls.