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34 replies to this topic

#1 Twinhelix

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Posted 14 June 2011 - 12:35 PM

Orginal text from this forum reads:

"Ok, so Teanchi and Beanchi are a married couple (dont ask me whose he and whose she)!

They have two kids, one of them is a girl, what is the probability that the other kid is also a girl.

Assume safely that the probability of each gender is 1/2.

Of course its not 1/2 else would make it a lousy puzzle..."

and then given and accepted answer in the puzzle is this:

Spoiler for Original Solution


Now my question is, is this solution correct?

So this is what I think, please correct me if I'm wrong because this one really puzzled me, even though it seems so simple.

Spoiler for What I think


Is my logic correct? Please elaborate. :)
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#2 shakingdavid

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Posted 14 June 2011 - 01:07 PM

Spoiler for explanation

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#3 sacohen0326

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Posted 14 June 2011 - 01:08 PM

Spoiler for I think the problem with your solution is


Spoiler for I guess my question, then, is

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#4 Plumbstar Tom

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Posted 14 June 2011 - 02:02 PM

Argue all you want but the information given to you about the first child helps in no way. The child is either a boy or a girl so it is 50% 1/2 however you put it.

Edited by Plumbstar Tom, 14 June 2011 - 02:02 PM.

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#5 KlueMaster

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Posted 14 June 2011 - 02:13 PM

Well, I always see it this way:
Spoiler for my way

Edited by KlueMaster, 14 June 2011 - 02:15 PM.

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#6 Gihan

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Posted 14 June 2011 - 03:07 PM

Well, I always see it this way:

Spoiler for my way


Spoiler for Good idea, but your maths is slightly wrong

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#7 sacohen0326

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Posted 14 June 2011 - 03:14 PM

Argue all you want but the information given to you about the first child helps in no way. The child is either a boy or a girl so it is 50% 1/2 however you put it.


But Plumbstar, the question is NOT "What is the probability that one of the children is a girl?" It is also not asking, "A mother gives birth to one child, and it is a girl. What is the probability that the second child will be a girl?" The question is "What is the probability that one child is a girl GIVEN THAT the other child is a girl?"

The trick here is to see that both children have already been born. They're both sitting in a room somewhere. The four possible combinations are:

Child 1 boy, Child 2 boy
Child 1 boy, Child 2 girl
Child 1 girl, Child 2 boy
Child 1 girl, Child 2 girl

We KNOW that one of them is a girl, so that immediately eliminates the first scenario. Of the remaining three, only one of them provides ANOTHER girl. That's where the 1/3 probability comes in.
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#8 shakingdavid

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Posted 14 June 2011 - 03:39 PM

Stop arguing, the problem is AMBIGUITY. All of you are right, you are just answering different questions. Let's turn this into two different non-ambiguous questions instead:

Spoiler for clearing it up

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#9 Twinhelix

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Posted 14 June 2011 - 03:42 PM

But Plumbstar, the question is NOT "What is the probability that one of the children is a girl?" It is also not asking, "A mother gives birth to one child, and it is a girl. What is the probability that the second child will be a girl?" The question is "What is the probability that one child is a girl GIVEN THAT the other child is a girl?"

The trick here is to see that both children have already been born. They're both sitting in a room somewhere. The four possible combinations are:

Child 1 boy, Child 2 boy
Child 1 boy, Child 2 girl
Child 1 girl, Child 2 boy
Child 1 girl, Child 2 girl

We KNOW that one of them is a girl, so that immediately eliminates the first scenario. Of the remaining three, only one of them provides ANOTHER girl. That's where the 1/3 probability comes in.



Okay, see, the trouble I'm having is that when you say there's a girl, the girl could either be Child 1 or Child 2 right? So surely the given girl could be Child 1 of the girl girl scenario OR Child 2 of the girl girl scenario. Help explain?
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#10 phillip1882

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Posted 14 June 2011 - 04:12 PM

this has been argued to death aleady. the answer is: it depends on the question being asked.
everyone is correct so far based on the reasoning they used.

shakingdavid has the right idea.

Spoiler for coin toss analogy

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