So here is the second thing that needs clearing up, if order does not matter then why are bg and gb different outcomes? If order does matter arent the outcomes bb, bb, bg, gb, gg, gg... which would still lead to a 50% chance its a boy.
Just look at big numbers. If there are hundred families with two kids, 25% of those will have two boys, 50% will have a boy and a girl, 25% will have two girls. There's no need to try to second guess that.
If you have trouble dealing with that, then you need an introductory course on probabilities and statistics. Highschool level.
It's pathetic that you think nobody else can think for themselves or come up with their own ideas and breakthroughs.
Do you honestly think that you can come up with the kind of breakthroughs that have been done in CS over the past 60 years without reading some of the literature?
Sure, if you write some simple scripts or basic applications, you don't need to know much about algorithms, but once you start messing about with algorithms and datastructures, it pays to at least have heard of Knuth.
Einstein didn't develop quantum mechanics, he was actually an opponent of it (his famous "god does not play dice" quote is a direct criticism of QM in fact).
It is of course a lot more complicated than that. He objected to some aspects of QM[*], but he also was the one who proposed the very first basics of what was to become QM, and he did quite a lot of work on it.
[*] The philosophical implications of the uncertainty and randomness, especially. He didn't deny the results, but he assumed there was some deterministic layer below it that would someday be discovered.
The question is incompletely phrased, which is entirely what TFA is about. Read it.
The simple point is this:
If you have selected a child, independent of gender, and that child happens to be a boy, then the gender of the other child is independent of this, and therefore has 50% change of being a boy.
If, on the other hand, you select a child specifically for being a boy and part of a 2-child family, then the gender of the other child is not independent.
In fact, it's even more complicated than that: do you select a 2-child families that has at least one boy, then 1/3 of those families will have 2 boys.
But if you take all 2-child families, and randomly pick a boy from all those children, then there's 50% change he's from a 2-boy family. Because they have twice as many boys, and therefore a bigger chance of being selected.
The famous 2-buy problem is about the middle option. TFA discusses the difference between the first and the second option, neglecting the third option. But a lot of people here seem to be focusing on the first and the third, and don't want to admit the legitimacy of the second option.
the boy MUST be either the younger or the older. Since he's either one or the other, we can infer that either b/g or b/g is also impossible.
No you can't, because you don't have that information. He can be either the older or the younger, or they can even be the same age. As long as you're not talking about a specifically identified boy, the chance is 1/3.
If he's older, then g/b is not possible, and if he's younger, then b/g is not possible.
But because we don't know, they're still both possible.
I'm still able to reach the site. Here's the entire text:
When intuition and math probably look wrong A twist on the Two Children Problem shows how information can steer what looks probable. By Julie Rehmeyer
I have two children, one of whom is a son born on a Tuesday. What is the probability that I have two boys?
Gary Foshee, a puzzle designer from Issaquah, Wash., posed this puzzle during his talk this past March at Gathering 4 Gardner, a convention of mathematicians, magicians and puzzle enthusiasts held biannually in Atlanta. The convention is inspired by Martin Gardner, the recreational mathematician, expositor and philosopher who died May 22 at age 95. Foshee’s riddle is a beautiful example of the kind of simple, surprising and sometimes controversial bits of mathematics that Gardner prized and shared with others.
“The first thing you think is ‘What has Tuesday got to do with it?’” said Foshee after posing his problem during his talk. “Well, it has everything to do with it.”
Even in that mathematician-filled audience, people laughed and shook their heads in astonishment.
When mathematician Keith Devlin of Stanford University later heard about the puzzle, he too initially thought the information about Tuesday should be irrelevant. But hearing that its provenance was the Gathering 4 Gardner conference, he studied it more carefully. He started first by recalling a simpler version of the question called the Two Children Problem, which Gardner himself posed in a Scientific American column in 1959. It leaves out the information about Tuesday entirely: Suppose that Mr. Smith has two children, at least one of whom is a son. What is the probability both children are boys?
Intuition would suggest that the answer should be 1/2, since the sex of one child is independent of the sex of the other. And indeed, had he been told which child was a boy (say, the younger one), this reasoning would be sufficient. But since the boy could be either the younger or the older child, the analysis is more subtle. Devlin started by listing the children’s sexes in the order of their birth:
Boy, girl Boy, boy Girl, boy
Since one child is a boy, we know that girl, girl isn’t a possibility. Of the three approximately equally likely possibilities, one has two boys and two have a girl and a boy — so the probability of two boys is 1/3, not 1/2, Devlin concluded.
He used this same method on the Tuesday birthday puzzle, enumerating the equally likely possibilities for the sex and birth day of each child and then counting them up.
If the older child is a boy born on Tuesday, there are 14 equally likely possibilities for the sex and birth day of his younger sibling: a girl born on any of the seven days of the week or a boy born on any of the seven days of the week. (This analysis ignores minor differences like the fact that slightly more babies are born on weekdays than on weekend days.)
Now suppose that the older child isn’t a boy born on Tuesday. The younger child then must be, of course. Now we count up the possibilities for the sex and birth day of the older child. If she’s a girl, she might have been born on any day of the week, generating seven more possibilities. If he’s a boy, he could have been born any day except Tuesday. (Otherwise this case would already have been counted in the first scenario: the older child a boy born on Tuesday). This second scenario generates just six, rather than seven, more possibilities.
Since each of these cases is (approximately) equally likely, we can compute the probability by dividing the number of cases in which there are two boys by the total number of cases. The total number of cases is 27: 14 if the older child is a boy born on Tuesday and 13 if the older child isn’t. In 13 of those cases both children are boys (7 if the older child is a boy born on Tuesday and 6 if he isn’t), yielding a probability of 13/27.
It's not purposely misleading English, it's just English. It's just that English (or any natural language) happens to be a poor medium for discussing statistics.
You're right! Pretty amazing, considering the article gives the correct answer and explains it pretty thoroughly. Even when you think: "But wait! Can't you look at it some other way?", the article does just that.
Read the article. Whether the answer is 50% or not depends on the context, and that context is not specified in the problem.
If you meet the person with his son, and he tells you that that son is born on a Tuesday, then the chance of the other kid being a boy is 50%. If you see him as one of the thousands of parents who have two children, at least of which is a boy who's born on a Tuesday, the chance of the other kid being a boy is 13/27.
Nazi war machine was so poorly organized that it lost to USSR in spite of the fact that Germany had much more industrial potential.
You're kidding, right? Nobody beats the Russia on its own soil. Napoleon's army was also very well organized, but that's just not enough to defeat Russia.
The German war machine at the start of WW2 was by far the best organized army in the world. The had the best trained officers, the best infantry tactics, the best panzer strategies. They made huge, extremely ambitious attack plans and executed them to perfection. Conquering most of western Europe in a matter of weeks is not something you do with a poorly organized army. Later in the war, when the allies had learned from the Germans, Russian war production came up to speed, the US joined the war and it became obvious that Germany had bitten off a lot more than it could chew, the German war machine started to break down. No doubt the unexpected setbacks in Russia played a big part in that.
"True love" is not just liking or loving someone alot. It's another level. If you haven't experienced it yourself, then you won't understand it. I have felt it, twice, yet I've had over 20 girlfriends, most of whom I simply loved.
I'm not sure what you mean by "true love", and how you distinguish it from lesser love. I suspect it's not the "mad storm of butterflies" in my stomach that I've experienced with two girls. It's the kind of physical response to love that makes you sick, unable to think clearly, and gives you a really, really weird feeling in your stomach. In any case, those two relationships were doomed. Didn't work at all for a variety of reasons. I'm currently married and love my wife deeply, but I never felt anything remotely like that storm of butterflies. It's much more rational, practical and plenty emotional too, but it lacks that weird way in which my body goes completely loopy. I don't miss it.
Relationships that work win out over crazy dysfunctional stuff every time, exciting though the craziness may be.
I wouldn't tell someone not to wear their wedding ring just because it is superficial.
Is this the right place to mention that I have only a wedding tattoo? It's a moebius strip (you know, two sides that are actually one) on the inside of the wrist. We went for the Escher "ants" version, but without the ants and the square holes in the strip.
Nerdy and simple, although it does look a bit like we belong to a secret society. Well, I guess we do, except it's not secret.
(My grandmother said: "That's awfully permanent". My response: "Isn't that the point of marriage?" Then she approved.)
The reason why nobody actually does this is because that way of life is stupefyingly difficult. Up before dawn to a full day of hard labor every single day.
Go spend a week on a real farm. Just a single week. I'm sure they'd be glad for the help. I'll bet you don't last two days. I doubt I would.
Farming really is ridiculously hard work, for ridiculously little profit. My brother-in-law has a farm (not in the US, mind you; perhaps things are better there) that's worth EUR 5 million; enough to retire from. But actually working the farm, he has to work 80 hours a week and barely makes ends meet. I live in one of the biggest agricultural exporting economies in the world, yet running a simple farm is not economically viable. There's something really wrong with our system.
Slashdot Mirror
So here is the second thing that needs clearing up, if order does not matter then why are bg and gb different outcomes? If order does matter arent the outcomes bb, bb, bg, gb, gg, gg... which would still lead to a 50% chance its a boy.
Just look at big numbers. If there are hundred families with two kids, 25% of those will have two boys, 50% will have a boy and a girl, 25% will have two girls. There's no need to try to second guess that.
If you have trouble dealing with that, then you need an introductory course on probabilities and statistics. Highschool level.
You want to tie it to the simcard, not to the phone.
Seems rather obvious, doesn't it? Rely on something that's reliable, rather than something that can be spoofed.
It's pathetic that you think nobody else can think for themselves or come up with their own ideas and breakthroughs.
Do you honestly think that you can come up with the kind of breakthroughs that have been done in CS over the past 60 years without reading some of the literature?
Sure, if you write some simple scripts or basic applications, you don't need to know much about algorithms, but once you start messing about with algorithms and datastructures, it pays to at least have heard of Knuth.
Newton's laws describe very accurately how gravity behaves on the Earth's surface, pretty much up to how the planets move around the Sun.
Except for Mercury. I don't know what exactly it was, but Mercury's orbit isn't quite right according to Newton's laws.
Einstein didn't develop quantum mechanics, he was actually an opponent of it (his famous "god does not play dice" quote is a direct criticism of QM in fact).
It is of course a lot more complicated than that. He objected to some aspects of QM[*], but he also was the one who proposed the very first basics of what was to become QM, and he did quite a lot of work on it.
[*] The philosophical implications of the uncertainty and randomness, especially. He didn't deny the results, but he assumed there was some deterministic layer below it that would someday be discovered.
The gambler's fallacy is irrelevant. The dice have already been rolled. What matters is how you select the dice that you get to see.
The question is incompletely phrased, which is entirely what TFA is about. Read it.
The simple point is this:
If you have selected a child, independent of gender, and that child happens to be a boy, then the gender of the other child is independent of this, and therefore has 50% change of being a boy.
If, on the other hand, you select a child specifically for being a boy and part of a 2-child family, then the gender of the other child is not independent.
In fact, it's even more complicated than that: do you select a 2-child families that has at least one boy, then 1/3 of those families will have 2 boys.
But if you take all 2-child families, and randomly pick a boy from all those children, then there's 50% change he's from a 2-boy family. Because they have twice as many boys, and therefore a bigger chance of being selected.
The famous 2-buy problem is about the middle option. TFA discusses the difference between the first and the second option, neglecting the third option. But a lot of people here seem to be focusing on the first and the third, and don't want to admit the legitimacy of the second option.
Excellent explanation! Especially the last bit.
the boy MUST be either the younger or the older. Since he's either one or the other, we can infer that either b/g or b/g is also impossible.
No you can't, because you don't have that information. He can be either the older or the younger, or they can even be the same age. As long as you're not talking about a specifically identified boy, the chance is 1/3.
If he's older, then g/b is not possible, and if he's younger, then b/g is not possible.
But because we don't know, they're still both possible.
Can't RTFA,
Yes you can. I just posted it as your GP.
I'm still able to reach the site. Here's the entire text:
When intuition and math probably look wrong
A twist on the Two Children Problem shows how information can steer what looks probable.
By Julie Rehmeyer
I have two children, one of whom is a son born on a Tuesday. What is the probability that I have two boys?
Gary Foshee, a puzzle designer from Issaquah, Wash., posed this puzzle during his talk this past March at Gathering 4 Gardner, a convention of mathematicians, magicians and puzzle enthusiasts held biannually in Atlanta. The convention is inspired by Martin Gardner, the recreational mathematician, expositor and philosopher who died May 22 at age 95. Foshee’s riddle is a beautiful example of the kind of simple, surprising and sometimes controversial bits of mathematics that Gardner prized and shared with others.
“The first thing you think is ‘What has Tuesday got to do with it?’” said Foshee after posing his problem during his talk. “Well, it has everything to do with it.”
Even in that mathematician-filled audience, people laughed and shook their heads in astonishment.
When mathematician Keith Devlin of Stanford University later heard about the puzzle, he too initially thought the information about Tuesday should be irrelevant. But hearing that its provenance was the Gathering 4 Gardner conference, he studied it more carefully. He started first by recalling a simpler version of the question called the Two Children Problem, which Gardner himself posed in a Scientific American column in 1959. It leaves out the information about Tuesday entirely: Suppose that Mr. Smith has two children, at least one of whom is a son. What is the probability both children are boys?
Intuition would suggest that the answer should be 1/2, since the sex of one child is independent of the sex of the other. And indeed, had he been told which child was a boy (say, the younger one), this reasoning would be sufficient. But since the boy could be either the younger or the older child, the analysis is more subtle. Devlin started by listing the children’s sexes in the order of their birth:
Boy, girl
Boy, boy
Girl, boy
Since one child is a boy, we know that girl, girl isn’t a possibility. Of the three approximately equally likely possibilities, one has two boys and two have a girl and a boy — so the probability of two boys is 1/3, not 1/2, Devlin concluded.
He used this same method on the Tuesday birthday puzzle, enumerating the equally likely possibilities for the sex and birth day of each child and then counting them up.
If the older child is a boy born on Tuesday, there are 14 equally likely possibilities for the sex and birth day of his younger sibling: a girl born on any of the seven days of the week or a boy born on any of the seven days of the week. (This analysis ignores minor differences like the fact that slightly more babies are born on weekdays than on weekend days.)
Now suppose that the older child isn’t a boy born on Tuesday. The younger child then must be, of course. Now we count up the possibilities for the sex and birth day of the older child. If she’s a girl, she might have been born on any day of the week, generating seven more possibilities. If he’s a boy, he could have been born any day except Tuesday. (Otherwise this case would already have been counted in the first scenario: the older child a boy born on Tuesday). This second scenario generates just six, rather than seven, more possibilities.
Since each of these cases is (approximately) equally likely, we can compute the probability by dividing the number of cases in which there are two boys by the total number of cases. The total number of cases is 27: 14 if the older child is a boy born on Tuesday and 13 if the older child isn’t. In 13 of those cases both children are boys (7 if the older child is a boy born on Tuesday and 6 if he isn’t), yielding a probability of 13/27.
Devlin w
No. I live in Europe and had no problem reading it.
To say the truth the problem is ill posed.
Well yeah, but that issue is already discussed in TFA.
It's not purposely misleading English, it's just English. It's just that English (or any natural language) happens to be a poor medium for discussing statistics.
Which explains exactly why the answer is 13/27.
You're right! Pretty amazing, considering the article gives the correct answer and explains it pretty thoroughly. Even when you think: "But wait! Can't you look at it some other way?", the article does just that.
Really, this time it pays to RTFA.
If you have a bowl of fruit, specifying that one of them is a banana could be done by picking one up and saying: "This is a banana."
5*5.25=26.25. Don't forget that pregnancy lasts 9 months.
(FF, FM, MF or MM)
FF is not possible
FM is not possible
Why is FM not possible? The M is a boy, isn't it?
Read the article. Whether the answer is 50% or not depends on the context, and that context is not specified in the problem.
If you meet the person with his son, and he tells you that that son is born on a Tuesday, then the chance of the other kid being a boy is 50%. If you see him as one of the thousands of parents who have two children, at least of which is a boy who's born on a Tuesday, the chance of the other kid being a boy is 13/27.
Nazi war machine was so poorly organized that it lost to USSR in spite of the fact that Germany had much more industrial potential.
You're kidding, right? Nobody beats the Russia on its own soil. Napoleon's army was also very well organized, but that's just not enough to defeat Russia.
The German war machine at the start of WW2 was by far the best organized army in the world. The had the best trained officers, the best infantry tactics, the best panzer strategies. They made huge, extremely ambitious attack plans and executed them to perfection. Conquering most of western Europe in a matter of weeks is not something you do with a poorly organized army. Later in the war, when the allies had learned from the Germans, Russian war production came up to speed, the US joined the war and it became obvious that Germany had bitten off a lot more than it could chew, the German war machine started to break down. No doubt the unexpected setbacks in Russia played a big part in that.
"True love" is not just liking or loving someone alot. It's another level. If you haven't experienced it yourself, then you won't understand it. I have felt it, twice, yet I've had over 20 girlfriends, most of whom I simply loved.
I'm not sure what you mean by "true love", and how you distinguish it from lesser love. I suspect it's not the "mad storm of butterflies" in my stomach that I've experienced with two girls. It's the kind of physical response to love that makes you sick, unable to think clearly, and gives you a really, really weird feeling in your stomach. In any case, those two relationships were doomed. Didn't work at all for a variety of reasons. I'm currently married and love my wife deeply, but I never felt anything remotely like that storm of butterflies. It's much more rational, practical and plenty emotional too, but it lacks that weird way in which my body goes completely loopy. I don't miss it.
Relationships that work win out over crazy dysfunctional stuff every time, exciting though the craziness may be.
I wouldn't tell someone not to wear their wedding ring just because it is superficial.
Is this the right place to mention that I have only a wedding tattoo? It's a moebius strip (you know, two sides that are actually one) on the inside of the wrist. We went for the Escher "ants" version, but without the ants and the square holes in the strip.
Nerdy and simple, although it does look a bit like we belong to a secret society. Well, I guess we do, except it's not secret.
(My grandmother said: "That's awfully permanent". My response: "Isn't that the point of marriage?" Then she approved.)
The reason why nobody actually does this is because that way of life is stupefyingly difficult. Up before dawn to a full day of hard labor every single day.
Go spend a week on a real farm. Just a single week. I'm sure they'd be glad for the help. I'll bet you don't last two days. I doubt I would.
Farming really is ridiculously hard work, for ridiculously little profit. My brother-in-law has a farm (not in the US, mind you; perhaps things are better there) that's worth EUR 5 million; enough to retire from. But actually working the farm, he has to work 80 hours a week and barely makes ends meet. I live in one of the biggest agricultural exporting economies in the world, yet running a simple farm is not economically viable. There's something really wrong with our system.