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#101
03-17-2005, 07:50 PM
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Re: Super Duper Extra Hard Brainteaser
[ QUOTE ]
What is the probability of girl named sarah, girl? 1/200 * 1/2 which is 100/40,000 Where am I going wrong? [/ QUOTE ] 1/200 * (99/100) * 1/2. They can't both be sarah. 
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#103
03-17-2005, 07:52 PM
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Re: Super Duper Extra Hard Brainteaser
[ QUOTE ]
[ QUOTE ] What is the probability of girl named sarah, girl? 1/200 * 1/2 which is 100/40,000 Where am I going wrong? [/ QUOTE ] 1/200 * (99/100) * 1/2. They can't both be sarah. [/ QUOTE ] Hmm. The probability of the first child being a girl called Sarah is just 1/200 and then the probability of the next one being a girl is 1/2 n'est pas?
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#104
03-17-2005, 07:53 PM
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Re: Super Duper Extra Hard Brainteaser
[ QUOTE ]
[ QUOTE ] [ QUOTE ] What is the probability of girl named sarah, girl? 1/200 * 1/2 which is 100/40,000 Where am I going wrong? [/ QUOTE ] 1/200 * (99/100) * 1/2. They can't both be sarah. [/ QUOTE ] Hmm. The probability of the first child being a girl called Sarah is just 1/200 and then the probability of the next one being a girl is 1/2 n'est pas? [/ QUOTE ] Non. Read this. All of it.
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#105
03-17-2005, 07:53 PM
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Re: Super Duper Extra Hard Brainteaser
[ QUOTE ]
jason, by that logic the answer to the first, easier, problem is 1/2, which is wrong. [/ QUOTE ] There are three possibilities once we know there is at least one girl: girl, girl boy, girl girl, boy Therefore the answer to the first question is 1/3
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#106
03-17-2005, 07:53 PM
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Re: Super Duper Extra Hard Brainteaser
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jason, by that logic the answer to the first, easier, problem is 1/2, which is wrong. [/ QUOTE ] Wrong, the possibilities in the first question, once we know there is at least one girl are G, B B, G G, G and all of these are equally likely. So the answer is 1/3.
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#107
03-17-2005, 07:54 PM
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Re: Super Duper Extra Hard Brainteaser
Seems to me that this is only a brainteaser because it induces people to waste a bunch of time with the Sarah red herring when the answer is still 1/3.
Think about it intuitively: If you gathered a population of mothers with two children, at least one of which is a girl, and divided them into subpopulations based on whether they had a child named Sarah, would you expect the subpopulations to have different estimated means on the #ofGirls variable. Basically, the Sarah thing just identifies a subpopulation but shouldn't change any other characteristics.
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#108
03-17-2005, 07:55 PM
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Re: Super Duper Extra Hard Brainteaser
[ QUOTE ]
Seems to me that this is only a brainteaser because it induces people to waste a bunch of time with the Sarah red herring when the answer is still 1/3. Think about intuitively: If you gathered a population of mothers with two children, at least one of which is a girl, and divided them into subpopulations based on whether one they had named a child Sarah, would you expect the subpopulations to have different estimated means on the #ofGirls variable. Basically, the Sarah thing just identifies a subpopulation but shouldn't change any other characteristics. [/ QUOTE ] Exactly.
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#109
03-17-2005, 07:56 PM
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Re: Super Duper Extra Hard Brainteaser
[ QUOTE ]
Seems to me that this is only a brainteaser because it induces people to waste a bunch of time with the Sarah red herring when the answer is still 1/3. Think about intuitively: If you gathered a population of mothers with two children, at least one of which is a girl, and divided them into subpopulations based on whether one they had named a child Sarah, would you expect the subpopulations to have different estimated means on the #ofGirls variable. Basically, the Sarah thing just identifies a subpopulation but shouldn't change any other characteristics. [/ QUOTE ] Think about it like this, it might change your mind: knowing that a women has two girls increases the likelihood that she has a child named Sarah. Conversely, knowing she has a child named Sarah....
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#110
03-17-2005, 07:56 PM
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Re: Super Duper Extra Hard Brainteaser
[ QUOTE ]
[ QUOTE ] [ QUOTE ] [ QUOTE ] What is the probability of girl named sarah, girl? 1/200 * 1/2 which is 100/40,000 Where am I going wrong? [/ QUOTE ] 1/200 * (99/100) * 1/2. They can't both be sarah. [/ QUOTE ] Hmm. The probability of the first child being a girl called Sarah is just 1/200 and then the probability of the next one being a girl is 1/2 n'est pas? [/ QUOTE ] Non. Read this. All of it. [/ QUOTE ] Please explain which part of what I said was wrong.
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