Super Duper Extra Hard Brainteaser

[gaming_mouse]

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Instead, I feel like a better approach would be to look at all the 2-child families and adjust my first assumption to something like "when a girl is born, there is an X% chance that she will be named Sarah, unless she already has a sister named Sarah" and set X such that the result is 1% of all girls are named Sarah.

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Under these assumptions, the solution offered by Patrick's professor is the correct one. However, he also had to assume the populations consisted entirely of 2 person families. Without some additional assumption like that, the above is still not enough info to solve the problem.

[Nomad84]

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Instead, I feel like a better approach would be to look at all the 2-child families and adjust my first assumption to something like "when a girl is born, there is an X% chance that she will be named Sarah, unless she already has a sister named Sarah" and set X such that the result is 1% of all girls are named Sarah.

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Under these assumptions, the solution offered by Patrick's professor is the correct one. However, he also had to assume the populations consisted entirely of 2 person families. Without some additional assumption like that, the above is still not enough info to solve the problem.

[/ QUOTE ]

I just worked out the problem using these assumptions and the one you just listed. I got 0.49874 also. I agree that the assumption the population consists entirely of 2 person families is an important one because obviously changing that assumption will change the value of X. I need to re-read the professor's response because I had a hard time following it the first time. I think that I basically followed the same thought process and assumptions that he used. I think the differences boiled down to me using X and him using p [img]/images/graemlins/tongue.gif[/img]

[gaming_mouse]

I agree that the assumption the population consists entirely of 2 person families is an important one because obviously changing that assumption will change the value of X.

It's also why I don't really like that answer.

IMO the best interpretation of the problem is the one where you set p=.01, and solve like that, even though this violates the 1% saras stipulation.

[Nomad84]

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I agree that the assumption the population consists entirely of 2 person families is an important one because obviously changing that assumption will change the value of X.

It's also why I don't really like that answer.

IMO the best interpretation of the problem is the one where you set p=.01, and solve like that, even though this violates the 1% saras stipulation.

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Using 0.01 along with the other assumptions that I made still gives approximately the same answer. For comparison, I found that using p=0.010025125787 with my assumptions gives an overall 1% Sarah's for a population consisting solely of 2-child families. I'm not sure if you meant solve the problem the same way that I already did, just using .01 for p or if you meant solving it differently, but using p=.01.

BTW, I had the same equations as the professor, it seems. He just simplified further than I did before plugging p back in.

[gaming_mouse]

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Using 0.01 along with the other assumptions that I made still gives approximately the same answer.

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Yes, sure, but at this point in the discussion the numerical answers have become all but irrelevant, IMO. The question has now become one of interpretation. I like the .01 interpretation pretty much just for the sake of simplicity. The professor's answer, and the additional assumptions it makes, just don't feel like the right answer for a brain teaser to me. Purely my opinion.

[Nomad84]

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The question has now become one of interpretation.

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Understood, and I have to agree with you.

[BOTW]

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IMO the best interpretation of the problem is the one where you set p=.01, and solve like that, even though this violates the 1% saras stipulation.

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As much as I respect you (and encourage you to continue to help everyone with great advice and proper math), I have to disagree. You can't just disregard a stipulation of the problem. I feel there are only two answers that can possibly be right, either 1/3 or 1/2. Any other answer forces "non-standard" assumptions or "trickery" and would better be called a riddle than a math or probability problem. (Even if only one girl is named Sarah in the whole world, what is the answer? What if half of them are? Or all of them?)

[omahahahaha]

100/99 !!!

[CardSharpCook]

Are you aware how easy this is? It is 50/50 in each example. That we know the first is a girl does not change the odds. I can't believe that I'm posting here, and I didn't read the whole thread, but you guys are way over thinking this.

[MasterShakes]

Question #1
Assuming equal chances of having a boy or a girl born to you, the answer is that 50% of the time she will have girl/boy, and 50% of the time she will have girl/girl. Knowing that she already had one girl changes nothing about the chances concerning the sex of the second child. There must be a girl in the pair, and the other child's sex will be 50/50.

Question #2
This question is poorly written. We have information concerning the naming tendencies of "mothers". However, we don't know whether the "woman" is a "mother" as well. In fact, it seems that the word "woman" was deliberately substituted.

Assuming, however, that the "woman" is the "mother" of both of the children she "has," the answer is the same as the first. The name of the girl doesn't matter. It's essentially the first question asked over again, and the answer remains the same - 50% girl/girl, 50% girl/boy.

I cannot see a way around this.