Heya:P
Boy this struck a nerve with me - you can read my comments in this story, by far my most prolific so far, to see my attempts to show some light to lemmingy people who assume that non-existing language opperators in the given question are the same as existing. Well, there is no "ONLY one of two kids". I don't see it.
The answer is always 1/2, because nowhere in question, if you read as per normal rules of grammar, is there any indication that the second child's gender depends on ANY outside parameters given in the question.
Thus there are only 2 possible solution sets -- boy boy and boy girl, which gives answer to the question and exact probability of 1/2, if we don't take into account random gender variations and possibility of more genders than 2.
And a cat:P
Read my other comments on this thread, where I try to expose these faux-mathematicians for the lawyers that they are -- as per normal, common sense wording (english and all) of the question, 1/2 is always the answer, because the other child is absolutely non-dependent on existing given constraints of the question. I suspect these particular mathematicians, lawyery as they are, seem to not really grasp proper use of language operators. I suspect they would make bad programmers.
Mind you, I met some nice mathematicians who share no such flaws, hence the partial defense on my part:P
> If someone says, "I have two children. One of them is a boy." The odds of the other one being a boy is 1/3.
No, it is 1/2.
I have 2 children a b
It does not matter the order, which of a or b is a boy. therefore just assign a to a boy.
a boy b ?
2 sets a boy b boy, a boy b girl.
Girl girl is thrown out previously, and it does not matter the which order the children are in. Girl-boy and boy-girl sets are EQUIVALENT in this case, because no contraindication is given that it is not the case. They are ONE set.
Therefore there are only two possible sets, boy-girl and boy-boy.
1/2.
The other people are too deeply sunk in the legalities of the wording of the question to realize that.
But the wording is actually non-ambigous.
If you'd want precision, you would say "only one of them is a boy born on Tuesday" for which, other existing solutions would be acceptable.
As per current wording, the answer is always, and will always remain, 1/2.
This is what I was trying to impart to deluded ones, it is so painful to watch people jumping off the cliff in lemming-like droves.
I wrote a fair share of well - reasoned comments, just because this article struck a deep nerve in me - about certain kind of people who always seem to conveniently (to themselves) misinterpret things.
Well, guess what, 1/2 is correct in all closed-universe cases with 1/2 gender normality and 2 genders.
PERIOD.
Glad to see I am not the only one not drawn in by this baroque nonsense:P
Exactly. This is what I have been trying to impart to people with my numerous comments, that there are only 2 possibility sets worth mentioning actually -- boy boy and boy girl. All others are unnecessary and not even hinted at by the even so "ambigous" wording of the question.
It is ALWAYS 1/2 in this case.*
* If we consider even gender distribution and absence of more sexes.
Well, I do not agree that boy - girl and girl - boy are not equivalent.
Rephrased without double negatives: I think there are only 2 groups, boy - boy and boy-girl. Importance of ordering is not at all discussed in the question, leaving us with only 2 sets.
Sorry, but I am not a lawyer - I interpret the question in the most simple way possible. Maybe this is where I am supposedly "wrong", but I do not care:P
The point is here, most improtantly, reducing the problem in a graceful manner. Nothing is known about the OTHER (not first or second, other) child. The state of the first child does not influence the state of un known child. Therefore, there are two possible sets of children -- boy boy and boy girl. Of the question "what is the probability of them both being boys", the correct answer will always be 1/2. Give or take a cat:P
Note that I will not change my mind or see the supposed light in this matter, because there is nothing to see, but the amount of delusion.
Note, if you do not allow them both to be born on Tuesday and them both being boys, you are doing it wrong.
One thing I'm wondering, is why those would be solvers do not take into account the possibility of hermaphrodite then ? Other "common sense" deviations ?
In the boundaries of the puzzle (2 genders, nothing known or assumed about other of the set of 2), so worded, the answer is and forever will be 1/2.
> I threw a coin twice yesterday. On one of those throws it landed up heads. What is the chance that the other throw also landed up heads?
Correction -- The question would be, what is the chance that they both landed up heads, and if one is known heads, there are only two sets, heads heads and heads (what we will call headless for this discussion). Otherwise, you're correct, and I am appaled at the state of discussion and people willingly putting up with verbal diarrhea and ambiguities to MIS explain a definition of simplicity in the form of a puzzle.
> The question is what is the chance that both kids have the same sex.
No, the question is what is the chance they're both boys ?
We know that one is a boy. Ordering and extraneous info is actually irrelevant. There are two possible sets -- boy boy and boy girl.
the chance is 1/2. Always. NO information is given about the second child, implicitly or explicitly. Anything else is mere trickery of the language -- "could have meant", etc. Logic has no place for ambiguity.
Hehe, yes, it is interesting how a mind is clouded by verbalities - I am not a native english speaker, and I looked at the problem - first instinct - why of course, 1/2.
Then, some arguments almost convinced me of those silly fractional probabilities.
Then I realised:
IFF is known that one of set a and b a is a boy, then, chance of 2 boys is 1/2, because it boils down to sets of a=boy b=boy, a=boy b=girl. Only two sets, ordering is NOT important to the task at hand. It is just a pile of verbal diarrhea, is all.
IFF is un known whether a or b is of any particular gender, then there exist 3 sets (a=boy b=boy, a=boy b=girl, a=girl b=girl), giving it a chance of 1/3.
Simple, unless you're a lwayer, which I'm starting to suspect many people are INTRINSICALLY.
P.S.: Also, if you want to imply that clause "one" of the boys is constricting, then the chance that there are 2 boys = 0, but I'm only lavyerbating here:P
> If we take a hypothetical something, call it "thing an sich" or "god" or whatever else you like, which has no effect on anything else, then due to it not affecting anything, we can not verify its existence. Also, its existence makes no difference whatsoever.
Ooh, so Nietzsche was on to virtual particles before mainstream science. Dammit, that guy was pretty badass.
God is Quantum Foam.
No, scratch that. Quantum Foam has way more influence on reality.
Well, my example was actually just that - an example for the sake of convenience, to extrapolate what would happen without law. I for one, would prefer much the good ole civil society. Of peace and mutual understanding.
Anyway, the whole argument is void without any real way to "measure power".
Without rules, the only thing between me and the solving of the garden slave problem would be a proper application of iron, which I, being extremely fit and intelligent, would not hesitate to do. In case of no rules, there would be no punishment by law. There would be locally applicated punishment by force, by lackeys of said fat cat, which can be easily overcome tho. Everybody sleeps once in a while.
Applied en masse, I would imagine the world wouold become something akin to the internet, with many power centers with locally enforced rules, by benevolent, or malevolent dictators (ala forums).
>"Beyond a critical point within a finite space, freedom diminishes as numbers increase. This is as >true of humans in the finite space of a planetary ecosystem as it is of gas molecules in a sealed >flask. The human question is not how many can possibly survive within the system, but what kind of >existence is possible for those who do survive." >- Frank Herbert, Dune
Have you read "The Dosadi Experiment" by Frank Herbert?
In that book he focuses entirely on this question, in a way.
Easily one of the most complex-written books I've read. Recommended:P
I really don't get how some people associate themSELVES with their meat. It's like they have no spirit. Maybe we (those of us who know about non-material origins of consciousness) are different in some way.
Slashdot Mirror
Heya :P
Boy this struck a nerve with me - you can read my comments in this story, by far my most prolific so far, to see my attempts to show some light to lemmingy people who assume that non-existing language opperators in the given question are the same as existing. Well, there is no "ONLY one of two kids". I don't see it.
The answer is always 1/2, because nowhere in question, if you read as per normal rules of grammar, is there any indication that the second child's gender depends on ANY outside parameters given in the question.
Thus there are only 2 possible solution sets -- boy boy and boy girl, which gives answer to the question and exact probability of 1/2, if we don't take into account random gender variations and possibility of more genders than 2.
And a cat :P
Read my other comments on this thread, where I try to expose these faux-mathematicians for the lawyers that they are -- as per normal, common sense wording (english and all) of the question, 1/2 is always the answer, because the other child is absolutely non-dependent on existing given constraints of the question. I suspect these particular mathematicians, lawyery as they are, seem to not really grasp proper use of language operators. I suspect they would make bad programmers. Mind you, I met some nice mathematicians who share no such flaws, hence the partial defense on my part :P
> If someone says, "I have two children. One of them is a boy." The odds of the other one being a boy is 1/3.
No, it is 1/2.
I have 2 children a b
It does not matter the order, which of a or b is a boy. therefore just assign a to a boy.
a boy b ?
2 sets a boy b boy, a boy b girl.
Girl girl is thrown out previously, and it does not matter the which order the children are in. Girl-boy and boy-girl sets are EQUIVALENT in this case, because no contraindication is given that it is not the case. They are ONE set.
Therefore there are only two possible sets, boy-girl and boy-boy.
1/2.
The other people are too deeply sunk in the legalities of the wording of the question to realize that.
But the wording is actually non-ambigous.
If you'd want precision, you would say "only one of them is a boy born on Tuesday" for which, other existing solutions would be acceptable.
As per current wording, the answer is always, and will always remain, 1/2.
This is what I was trying to impart to deluded ones, it is so painful to watch people jumping off the cliff in lemming-like droves.
I wrote a fair share of well - reasoned comments, just because this article struck a deep nerve in me - about certain kind of people who always seem to conveniently (to themselves) misinterpret things.
Well, guess what, 1/2 is correct in all closed-universe cases with 1/2 gender normality and 2 genders.
PERIOD.
Glad to see I am not the only one not drawn in by this baroque nonsense :P
> What we can deduce from the wording is that his other child is not a son born on a tuesday.
No we can not - nowhere it is shown, in the wording of the question, to be the case.
In fact, NOTHING is mentioned, or is known about the other child.
http://slashdot.org/comments.pl?sid=1701394&cid=32729366
http://slashdot.org/comments.pl?sid=1701394&cid=32729694
http://slashdot.org/comments.pl?sid=1701394&cid=32729826
Exactly. This is what I have been trying to impart to people with my numerous comments, that there are only 2 possibility sets worth mentioning actually -- boy boy and boy girl. All others are unnecessary and not even hinted at by the even so "ambigous" wording of the question.
It is ALWAYS 1/2 in this case.*
* If we consider even gender distribution and absence of more sexes.
Well, I do not agree that boy - girl and girl - boy are not equivalent.
Rephrased without double negatives: I think there are only 2 groups, boy - boy and boy-girl. Importance of ordering is not at all discussed in the question, leaving us with only 2 sets.
Sorry, but I am not a lawyer - I interpret the question in the most simple way possible. Maybe this is where I am supposedly "wrong", but I do not care :P
See my other reply - I formalized the problem in a different, yet straightforwarde way, and lo and behold, my answer is also 1/2.
:P
http://slashdot.org/comments.pl?sid=1701394&cid=32729366
The point is here, most improtantly, reducing the problem in a graceful manner. Nothing is known about the OTHER (not first or second, other) child. The state of the first child does not influence the state of un known child. Therefore, there are two possible sets of children -- boy boy and boy girl. Of the question "what is the probability of them both being boys", the correct answer will always be 1/2. Give or take a cat
Note that I will not change my mind or see the supposed light in this matter, because there is nothing to see, but the amount of delusion.
Note, if you do not allow them both to be born on Tuesday and them both being boys, you are doing it wrong.
Exactly...
One thing I'm wondering, is why those would be solvers do not take into account the possibility of hermaphrodite then ? Other "common sense" deviations ?
In the boundaries of the puzzle (2 genders, nothing known or assumed about other of the set of 2), so worded, the answer is and forever will be 1/2.
> I threw a coin twice yesterday. On one of those throws it landed up heads. What is the chance that the other throw also landed up heads?
Correction -- The question would be, what is the chance that they both landed up heads, and if one is known heads, there are only two sets, heads heads and heads (what we will call headless for this discussion). Otherwise, you're correct, and I am appaled at the state of discussion and people willingly putting up with verbal diarrhea and ambiguities to MIS explain a definition of simplicity in the form of a puzzle.
> The question is what is the chance that both kids have the same sex.
No, the question is what is the chance they're both boys ?
We know that one is a boy. Ordering and extraneous info is actually irrelevant. There are two possible sets -- boy boy and boy girl.
the chance is 1/2. Always. NO information is given about the second child, implicitly or explicitly. Anything else is mere trickery of the language -- "could have meant", etc. Logic has no place for ambiguity.
> He might be. The question does not say one way or the other.
What is the probability of that ?
If the parent has two boys born on a Tuesday, he could equally have declared the other boy as being born on a Tuesday.
What is the probability of that ?
Hehe, yes, it is interesting how a mind is clouded by verbalities - I am not a native english speaker, and I looked at the problem - first instinct - why of course, 1/2.
Then, some arguments almost convinced me of those silly fractional probabilities.
Then I realised:
IFF is known that one of set a and b a is a boy, then, chance of 2 boys is 1/2, because it boils down to sets of a=boy b=boy, a=boy b=girl. Only two sets, ordering is NOT important to the task at hand. It is just a pile of verbal diarrhea, is all.
IFF is un known whether a or b is of any particular gender, then there exist 3 sets (a=boy b=boy, a=boy b=girl, a=girl b=girl), giving it a chance of 1/3.
Simple, unless you're a lwayer, which I'm starting to suspect many people are INTRINSICALLY.
P.S.: Also, if you want to imply that clause "one" of the boys is constricting, then the chance that there are 2 boys = 0, but I'm only lavyerbating here :P
OR, how many times it can successively explode, which would also be quite impressive. And surprising.
> Kids are made by biological events, not given by a supreme being.
Kids are made BY momma and poppa. And lotsa love.
> If we take a hypothetical something, call it "thing an sich" or "god" or whatever else you like, which has no effect on anything else, then due to it not affecting anything, we can not verify its existence. Also, its existence makes no difference whatsoever.
Ooh, so Nietzsche was on to virtual particles before mainstream science. Dammit, that guy was pretty badass.
God is Quantum Foam.
No, scratch that. Quantum Foam has way more influence on reality.
Of course ! If there's a glaspipe around, there should be a sufficient motivation for it to hop around and light one UP ! :P
Well, my example was actually just that - an example for the sake of convenience, to extrapolate what would happen without law. I for one, would prefer much the good ole civil society. Of peace and mutual understanding.
Anyway, the whole argument is void without any real way to "measure power".
It's over 9000, btw :P
Without rules, the only thing between me and the solving of the garden slave problem would be a proper application of iron, which I, being extremely fit and intelligent, would not hesitate to do. In case of no rules, there would be no punishment by law. There would be locally applicated punishment by force, by lackeys of said fat cat, which can be easily overcome tho. Everybody sleeps once in a while.
Applied en masse, I would imagine the world wouold become something akin to the internet, with many power centers with locally enforced rules, by benevolent, or malevolent dictators (ala forums).
will be a bitch tho :)
>"Beyond a critical point within a finite space, freedom diminishes as numbers increase. This is as >true of humans in the finite space of a planetary ecosystem as it is of gas molecules in a sealed >flask. The human question is not how many can possibly survive within the system, but what kind of >existence is possible for those who do survive."
:P
>- Frank Herbert, Dune
Have you read "The Dosadi Experiment" by Frank Herbert?
In that book he focuses entirely on this question, in a way.
Easily one of the most complex-written books I've read. Recommended
You tell em.
I really don't get how some people associate themSELVES with their meat.
It's like they have no spirit.
Maybe we (those of us who know about non-material origins of consciousness) are different in some way.
"Goblin Reservation", by Clifford Simak.
And amazingly good book.
Few? Are you nuts?
This is Slashdot, everyone knows Fermat here.