Super Duper Extra Hard Brainteaser - Page 20

jason_t · #**191** 03-17-2005, 09:45 PM

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I also have a MS in statistics. But I'm assuming Patrick wants something more independent than that, which is fair. I'm offering suggestions, but he's not taking...

Welshing on a bet is not cool.

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Yeah, I understand that. That's why I prefaced with "FWIW."

gaming_mouse · #**192** 03-17-2005, 09:47 PM

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Mouse, please give me your answer, using your equation, if the chance of a girl being named Sarah was 99% or 100%, so I can stop feeling stupid.

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If 99%, the answer is the same.

100% is a contradiction, because then the other child has to be a boy, since you can't have two girls named sara. That is, the answer would be 0.

hoyaboy1 · #**193** 03-17-2005, 09:49 PM

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Mouse, please give me your answer, using your equation, if the chance of a girl being named Sarah was 99% or 100%, so I can stop feeling stupid.

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If 99%, the answer is the same.

100% is a contradiction, because then the other child has to be a boy, since you can't have two girls named sara. That is, the answer would be 0.

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Why can't the equation adjust for the 100%?

And I simply can't see how if it is 99% the answer would still be 50%. How could the 99 Sarahs out of 100 have a 50% chance of having a sister who is 1/100?

jason_t · #**194** 03-17-2005, 09:50 PM

The answer won't change because of the conditional probabilities.

mostsmooth · #**195** 03-17-2005, 09:51 PM

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Mouse, please give me your answer, using your equation, if the chance of a girl being named Sarah was 99% or 100%, so I can stop feeling stupid.

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If 99%, the answer is the same.

100% is a contradiction, because then the other child has to be a boy, since you can't have two girls named sara. That is, the answer would be 0.

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now im confused (as if i wasnt already), your saying that if 99% of girls were named sarah, and a woman had a girl named sarah, its ~50/50 the other kid is a girl?
this doesnt seem right, not even close to right

hoyaboy1 · #**196** 03-17-2005, 09:52 PM

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?

Keats13 · #**197** 03-17-2005, 09:52 PM

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OK right. Lets assume 1,000,000 families.

250,000 will be 2 boys
250,000 willl be 2 girls
500,000 will be one of each.

Of the 500,000 with 1 boy, 1 girl, there will be 5,000 instances where the girl is Sarah.

Of the 250,000 instances with 2 girls, there will be 4975 instances with a girl named Sarah.

Therefore there is a 4975/9975 (199/399) chance that the mother has 2 girls.

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In this case, there are 1 million girls. And there are 9975 Sarahs. This is not 1/100. Your solution violates one of the assumptions.

Edit: nevermind, I'm an idiot. The limit as the # of families increases is 1/100. Sorry.

gaming_mouse · #**198** 03-17-2005, 09:53 PM

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And I simply can't see how if it is 99% the answer would still be 50%. How could the 99 Sarahs out of 100 have a 50% chance of having a sister who is 1/100?

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The sister only has to be a girl, 50%

As for the equation, it's not a matter of adjusting. By the assumption of the puzzle, it is impossible to have two girls named Sara. So if all girls are named Sara, the woman can have only 1 girl. This has nothing to do with probability. It's just logic.

hoyaboy1 · #**199** 03-17-2005, 09:54 PM

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And I simply can't see how if it is 99% the answer would still be 50%. How could the 99 Sarahs out of 100 have a 50% chance of having a sister who is 1/100?

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The sister only has to be a girl, 50%

As for the equation, it's not a matter of adjusting. By the assumption of the puzzle, it is impossible to have two girls named Sara. So if all girls are named Sara, the woman can have only 1 girl. This has nothing to do with probability. It's just logic.

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Please read my above post about 1000 girls and clear up whatever I am missing.

partygirluk · #**200** 03-17-2005, 09:58 PM

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OK right. Lets assume 1,000,000 families.

250,000 will be 2 boys
250,000 willl be 2 girls
500,000 will be one of each.

Of the 500,000 with 1 boy, 1 girl, there will be 5,000 instances where the girl is Sarah.

Of the 250,000 instances with 2 girls, there will be 4975 instances with a girl named Sarah.

Therefore there is a 4975/9975 (199/399) chance that the mother has 2 girls.

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In this case, there are 1 million girls. And there are 9975 Sarahs. This is not 1/100. Your solution violates one of the assumptions.

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There cant be 2 sarahs