Quick Logic Problem

KingCondanomation said:
So following your logic, say I were to ask all those parents in the world who have 2 kids and that at least 1 of them is a boy, if both children they have are boys? You are saying that roughly half the respondents would say they had both boys, and the other half would say they had one boy and one girl?
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yes. You're catching on.
 
KingCondanomation said:
1 child's sex is known but BOTH children's relation to Jane are not known.

Try this:
If everyone on this board had 2 kids and I asked all those who have at least 1 boy, how many of you have 2 boys? The response would be about a third.

Just like if everyone on this board had 2 kids and I asked all those who have at least 1 girl, how many of you have 2 girls? The response would also be about a third.
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Really??? So if a about a third (which doesn't exist) have two boys then two thirds would have a boy and a girl?
 
KingCondanomation said:
So following your logic, say I were to ask all those parents in the world who have 2 kids and that at least 1 of them is a boy, if both children they have are boys? You are saying that roughly half the respondents would say they had both boys, and the other half would say they had one boy and one girl?
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No, I am saying that mathematically, if we know one is a boy it doesn't change the probability that the other is a boy at all. It doesn't even matter if we know that the first one was a boy or don't. We know that only one child is unknown and that there are two possibilities with an equal chance of each possibility.

No matter when the unknown child was born, it's probability of being a girl or a boy doesn't change.

And it's "logic" only in it is the correct way to figure the problem.

If you were in my statistics class and tried to come up with your chart it would still be the wrong answer.
 
Darla said:
Could this be the most boring thread ever?
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I don't know. It's kind of hilarious that Dano posed a logic problem in the first place and it's even more humorous that he got his own logic problem wrong. Funnier still is that continues to insist that he is correct.
 
Damocles said:
No, I am saying that mathematically, if we know one is a boy it doesn't change the probability that the other is a boy at all. It doesn't even matter if we know that the first one was a boy or don't. We know that only one child is unknown and that there are two possibilities with an equal chance of each possibility.

No matter when the unknown child was born, it's probability of being a girl or a boy doesn't change.

And it's "logic" only in it is the correct way to figure the problem.

If you were in my statistics class and tried to come up with your chart it would still be the wrong answer.
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Which other though? You are thinking of this in terms of one and then the next.

What is your answer to the below:
Say I were to ask all those parents in the world who have 2 kids and that at least 1 of them is a boy, if both children they have are boys? You are saying that roughly half the respondents would say they had both boys, and the other half would say they had one boy and one girl?
 
KingCondanomation said:
Which other though? You are thinking of this in terms of one and then the next.

What is your answer to the below:
Say I were to ask all those parents in the world who have 2 kids and that at least 1 of them is a boy, if both children they have are boys? You are saying that roughly half the respondents would say they had both boys, and the other half would say they had one boy and one girl?
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Again, you are taking the superfluous and attempting to make it salient.

It is not salient to the problem at all.

There is one child whose sex is unknown, the chances of that sex being a boy is 50% regardless of your chart. One variable, two possibilities, equal probability for each possibility = 50% no matter how many lines it fills on a chart.

And it doesn't matter what a group of people would say. That doesn't change the probability one iota either.
 
king. Its one and then the other. one is boy, the other is unknown. There's a 50/50 chance the other is also a boy. times 2 ladies, that's .25.
 
KingCondanomation said:
Which other though? You are thinking of this in terms of one and then the next.

What is your answer to the below:
Say I were to ask all those parents in the world who have 2 kids and that at least 1 of them is a boy, if both children they have are boys? You are saying that roughly half the respondents would say they had both boys, and the other half would say they had one boy and one girl?
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Yes. Do your own math or read post #102.

It has to be half. You stated that abour 1/3 would say they had two boys. That means that 2/3 would have to have a boy and a girl by your logic. There are no other options left.
 
Dungheap said:
I don't know. It's kind of hilarious that Dano posed a logic problem in the first place and it's even more humorous that he got his own logic problem wrong. Funnier still is that continues to insist that he is correct.
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I am right and I may as well end this making Dung the dunce, as this was never my logic problem, I lifted it off a similar problem posed to the smartest woman in the world.


"Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys? My algebra teacher insists that the probability is greater that the man has two boys, but I think the chances may be the same. What do you think?

Vos Savant agreed with the algebra teacher, writing that the chances are only 1 out of 3 that the woman has two boys, but 1 out of 2 that the man has two boys. Readers argued for 1 out of 2 in both cases, prompting multiple follow-ups. Finally vos Savant started a survey, calling on women readers with exactly two children and at least one boy to tell her the sex of both children. With almost eighteen thousand responses, the results showed 35.9% (a little over 1 in 3) with two boys.
http://en.wikipedia.org/wiki/Marilyn_vos_Savant#.22Two_boys.22_problem

(Note that I changed it from Man and Woman to Jane and Joan as I thought it would be easier to understand)
 
A survey does not equate to the probability of the variable.

If a survey was taken that said that most people thought light was slower than sound would it change the probability of them being wrong?

Simply stated, the survey showed that most people have no idea what they are doing in math, it doesn't change that the probability is still 25%. And that has to be the stupidest Algebra teacher ever if she says that the probability changes because of birth order.
 
Dungheap said:
I don't know. It's kind of hilarious that Dano posed a logic problem in the first place and it's even more humorous that he got his own logic problem wrong. Funnier still is that continues to insist that he is correct.
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Oh and it's duly noted that the Liberals on here (Dung, Onceler, Darla) stayed out of trying to make any guesses, wonder why that would be? :rolleyes:
 
KingCondanomation said:
I am right and I may as well end this making Dung the dunce, as this was never my logic problem, I lifted it off a similar problem posed to the smartest woman in the world.


"Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys? My algebra teacher insists that the probability is greater that the man has two boys, but I think the chances may be the same. What do you think?

Vos Savant agreed with the algebra teacher, writing that the chances are only 1 out of 3 that the woman has two boys, but 1 out of 2 that the man has two boys. Readers argued for 1 out of 2 in both cases, prompting multiple follow-ups. Finally vos Savant started a survey, calling on women readers with exactly two children and at least one boy to tell her the sex of both children. With almost eighteen thousand responses, the results showed 35.9% (a little over 1 in 3) with two boys.
http://en.wikipedia.org/wiki/Marilyn_vos_Savant#.22Two_boys.22_problem

(Note that I changed it from Man and Woman to Jane and Joan as I thought it would be easier to understand)
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Sampling error.
 
KingCondanomation said:
I am right and I may as well end this making Dung the dunce, as this was never my logic problem, I lifted it off a similar problem posed to the smartest woman in the world.


"Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys? My algebra teacher insists that the probability is greater that the man has two boys, but I think the chances may be the same. What do you think?

Vos Savant agreed with the algebra teacher, writing that the chances are only 1 out of 3 that the woman has two boys, but 1 out of 2 that the man has two boys. Readers argued for 1 out of 2 in both cases, prompting multiple follow-ups. Finally vos Savant started a survey, calling on women readers with exactly two children and at least one boy to tell her the sex of both children. With almost eighteen thousand responses, the results showed 35.9% (a little over 1 in 3) with two boys.
http://en.wikipedia.org/wiki/Marilyn_vos_Savant#.22Two_boys.22_problem

(Note that I changed it from Man and Woman to Jane and Joan as I thought it would be easier to understand)
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SO TWO THIRDS had a boy and a girl?
 
Damocles said:
A survey does not equate to the probability of the variable.

If a survey was taken that said that most people thought light was slower than sound would it change the probability of them being wrong?

Simply stated, the survey showed that most people have no idea what they are doing in math, it doesn't change that the probability is still 25%. And that has to be the stupidest Algebra teacher ever if she says that the probability changes because of birth order.
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It's more than a survey and she is not quizzing people on their knowledge which of course is far more fallible.
Read the link and view the table, you will see.
 
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