Wanna debate a math problem?
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24-02-2012, 01:07 AM
RE: Wanna debate a math problem?
(24-02-2012 12:53 AM)Azaraith Wrote:  
(24-02-2012 12:42 AM)kim Wrote:  
(24-02-2012 12:16 AM)Azaraith Wrote:  
(23-02-2012 04:36 PM)daylightisabadthing Wrote:  All possible combinations : BB BG GB GG

The older child is a girl rules out BB and BG leaving 2 possibilities so the chance 50%.

One of the children is a boy rules out GG leaving 3 possibilities so the chance is 33.3%

But why does order matter? IMO, from the initial question, GB = BG. There'd only be two options there - a family with one boy and one girl or a family with two boys. (GB/BG or BB). There isn't any reason from the initial question that the age of the children is a factor... I see where they are coming from, but unless order of birth is a part of the question, I don't see how it's adding an additional possibility besides boy + boy or boy + girl. It's a possible arrangement, but if we're just trying to guess the probability that both are male the order doesn't matter... Could we also throw in the possibility that one is a hermaphrodite? That one is transgender and identifies as a female, though born with male parts? You could make the probability quite low by adding "possible scenarios" like that...

The question is about the number of possibilities that will go into this one choice.

In each group of two children, we already know one of those two is a boy. So...

We have the boy and a boy. This is one possibility.
We have the boy and a girl. This is one possibility.
We have the boy and a child of unknown sex -could be boy or girl. This is one possibility.

There are three possibilities for this one choice.
1/3 = 33.3%
Dodgy

But along the same logic, there's the possibility that the other child would be a hermaphrodite or transexual, so are we to include those too and make the probability 20% instead? (since hermaphrodite and transgender aren't "unknown sex") Or are we grouping them into "unknown sex" as an "other" category???

It's not unknown sex... it is a child whom is either a boy or is a girl... we simply do not know ... it has nothing to do with sex.... it's about the possibilities available... This is random possibility

We could do the same thing with cats and dogs...

In each group of two animals, we already know one of those two is a dog. So...

We have the dog and a dog. This is one possibility.
We have the dog and a cat. This is one possibility.
We have the dog and an animal(random) -could be dog or could be a cat. This is one possibility.

There are three possibilities for this one choice.
1/3 = 33.3%

Got it?

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24-02-2012, 04:09 AM
RE: Wanna debate a math problem?
(24-02-2012 01:07 AM)kim Wrote:  
(24-02-2012 12:53 AM)Azaraith Wrote:  
(24-02-2012 12:42 AM)kim Wrote:  
(24-02-2012 12:16 AM)Azaraith Wrote:  
(23-02-2012 04:36 PM)daylightisabadthing Wrote:  All possible combinations : BB BG GB GG

The older child is a girl rules out BB and BG leaving 2 possibilities so the chance 50%.

One of the children is a boy rules out GG leaving 3 possibilities so the chance is 33.3%

But why does order matter? IMO, from the initial question, GB = BG. There'd only be two options there - a family with one boy and one girl or a family with two boys. (GB/BG or BB). There isn't any reason from the initial question that the age of the children is a factor... I see where they are coming from, but unless order of birth is a part of the question, I don't see how it's adding an additional possibility besides boy + boy or boy + girl. It's a possible arrangement, but if we're just trying to guess the probability that both are male the order doesn't matter... Could we also throw in the possibility that one is a hermaphrodite? That one is transgender and identifies as a female, though born with male parts? You could make the probability quite low by adding "possible scenarios" like that...

The question is about the number of possibilities that will go into this one choice.

In each group of two children, we already know one of those two is a boy. So...

We have the boy and a boy. This is one possibility.
We have the boy and a girl. This is one possibility.
We have the boy and a child of unknown sex -could be boy or girl. This is one possibility.

There are three possibilities for this one choice.
1/3 = 33.3%
Dodgy

But along the same logic, there's the possibility that the other child would be a hermaphrodite or transexual, so are we to include those too and make the probability 20% instead? (since hermaphrodite and transgender aren't "unknown sex") Or are we grouping them into "unknown sex" as an "other" category???

It's not unknown sex... it is a child whom is either a boy or is a girl... we simply do not know ... it has nothing to do with sex.... it's about the possibilities available... This is random possibility

We could do the same thing with cats and dogs...

In each group of two animals, we already know one of those two is a dog. So...

We have the dog and a dog. This is one possibility.
We have the dog and a cat. This is one possibility.
We have the dog and an animal(random) -could be dog or could be a cat. This is one possibility.

There are three possibilities for this one choice.
1/3 = 33.3%

Got it?


No, I don't think that came in to play at all actually. The permutations BB BG GB GG are the only things that are considered. Granted they probabaly should consider more... dang it, the computer I'm using right now doesn't have spell check. That's what I get for forgetting my jump drive... The only one that is eliminated is GG if one of them was a boy. Just like the rewording states: "Mr. Smith says: 'I have two children and it is not the case that they are both girls.' Given this information, what is the probability that both children are boys?".. this specifically states that the case with two girls is out.

Why is BG and GB not the same? Granted, like they said in the article, the wording is ambiguous, but even then they don't consider BG and GB the same. I think the wording that says "older child" gives the clue. One is older and one is younger. So BG is the older boy and younger girl, while GB is older girl and younger boy (or vise versa, as long as it's all in one direction).

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24-02-2012, 08:12 AM
RE: Wanna debate a math problem?
I'm still holding strong on the fact that if you ask the probabliity that the other child is a boy or girl the answer is 50%.

If you ask the probablity of having 2 boys or 2 girls the answer is 25%.

If you know that one is a boy and then ask the probablity of them having another boy, that goes back to the question of chances of the other child being a boy or girl. 50%.

If you already have a boy then the chances of having another one are 50% since you can only have either another boy or a girl.

“Whenever you find yourself on the side of the majority, it's time to pause and reflect.”

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24-02-2012, 08:30 AM
RE: Wanna debate a math problem?
(24-02-2012 08:12 AM)germanyt Wrote:  I'm still holding strong on the fact that if you ask the probabliity that the other child is a boy or girl the answer is 50%.

If you ask the probablity of having 2 boys or 2 girls the answer is 25%.

If you know that one is a boy and then ask the probablity of them having another boy, that goes back to the question of chances of the other child being a boy or girl. 50%.

If you already have a boy then the chances of having another one are 50% since you can only have either another boy or a girl.

You are correct, if you know one, then the other is 50%, but we don't really know.

For instance, when we know that the older sister is older, then we automatically know that the first child is female:

BG and BB aren't valid, that leaves GB and GG. It will be a boy or a girl next, so 50%.

If don't know either, then yeah it's either BB BG GB or GG, so any one of those is 25%, so if I ask what the percentage of having at least one girl in two kids would be 3/4 or 75% chance.

However, we know the sex of one of the kids, but we don't know which from the chances of: BB BG GB or GG.. automatically, we don't have a chance of GG and only BB, BG, or GB, but not which one. You have a 66.7% chance of having a girl if one of the kids is a boy (but don't know which). If we know which, that percentage drops to 50%. (correct me if I'm wrong). That leaves only 33.3% chance of having two boys if you know one is going to be a boy already. That's the reason for the difference in percent from what you expect, not that other sexes are in play. If you add other sexes, then the percentages probably would change differently from what you'd expect.

Sometimes statistics doesn't match what is "common sense". Take a look at the Monty Hall problem which was argued against by a lot of very intelligent people, only to be proven wrong by the data and actually running tests. This is a problem you can test yourself and see that the results are counter to common sense (assuming you think opposing to the statistics).

We may even be able to set up a test case for this problem as well that can be tested... Well, depending on who isn't too lazy or busy of course.

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24-02-2012, 08:51 AM
RE: Wanna debate a math problem?
(24-02-2012 08:30 AM)craniumonempty Wrote:  
(24-02-2012 08:12 AM)germanyt Wrote:  I'm still holding strong on the fact that if you ask the probabliity that the other child is a boy or girl the answer is 50%.

If you ask the probablity of having 2 boys or 2 girls the answer is 25%.

If you know that one is a boy and then ask the probablity of them having another boy, that goes back to the question of chances of the other child being a boy or girl. 50%.

If you already have a boy then the chances of having another one are 50% since you can only have either another boy or a girl.

You are correct, if you know one, then the other is 50%, but we don't really know.

For instance, when we know that the older sister is older, then we automatically know that the first child is female:

BG and BB aren't valid, that leaves GB and GG. It will be a boy or a girl next, so 50%.

If don't know either, then yeah it's either BB BG GB or GG, so any one of those is 25%, so if I ask what the percentage of having at least one girl in two kids would be 3/4 or 75% chance.

However, we know the sex of one of the kids, but we don't know which from the chances of: BB BG GB or GG.. automatically, we don't have a chance of GG and only BB, BG, or GB, but not which one. You have a 66.7% chance of having a girl if one of the kids is a boy (but don't know which). If we know which, that percentage drops to 50%. (correct me if I'm wrong). That leaves only 33.3% chance of having two boys if you know one is going to be a boy already. That's the reason for the difference in percent from what you expect, not that other sexes are in play. If you add other sexes, then the percentages probably would change differently from what you'd expect.

Sometimes statistics doesn't match what is "common sense". Take a look at the Monty Hall problem which was argued against by a lot of very intelligent people, only to be proven wrong by the data and actually running tests. This is a problem you can test yourself and see that the results are counter to common sense (assuming you think opposing to the statistics).

We may even be able to set up a test case for this problem as well that can be tested... Well, depending on who isn't too lazy or busy of course.


I agree. If we already know that one is a boy then it eliminates the 50% of the first child being a boy. So we only have to figure the odds, not of the 2nd child being a boy (would be 50%) but the chances of ending up with 2 boys (weird how that is two different things mathmatically).

“Whenever you find yourself on the side of the majority, it's time to pause and reflect.”

-Mark Twain
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24-02-2012, 02:22 PM
RE: Wanna debate a math problem?
(24-02-2012 08:51 AM)germanyt Wrote:  I agree. If we already know that one is a boy then it eliminates the 50% of the first child being a boy. So we only have to figure the odds, not of the 2nd child being a boy (would be 50%) but the chances of ending up with 2 boys (weird how that is two different things mathmatically).

Hmm, not quite. If we know one is a boy and know which one, Then that leaves only one position and 50% chance of boy or girl. If we know one is a boy, but don`t know which, but at least one is a boy, then that means that we can only eliminate them both being girls (GG), but we can't eliminate them both being boys (BB), older boy/younger girl (BG), or older girl/younger boy (GB).

Before we figure the chances of ending up with 2 boys we must set the stage. We know that at least one is a boy, so 2 girls is out that leaves GB BG BB. What is the probability of having one girl if at least one is a boy? That would be 66.7% ( 2 out of 3 shot ). Leaving the one where we have two boys. The chances of having two boys would be 33.3%..

The statistics behind this are a little more complicated then just listing the permutations. I could brush up and try to explain them though. It's been a while since I had to deal with statistics.

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24-02-2012, 05:21 PM
RE: Wanna debate a math problem?
I had an entire college course devoted to random probability; the course was called Principles of Mathematics and was only available post college algebra. I loved it so much, I kept the text. It was always beautiful before... but it was in that class when math began to become extremely elegant to me. Heart
Quite probably, one of the first semesters in my life that my favorite class was a math class. Shy

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25-02-2012, 08:24 AM
RE: Wanna debate a math problem?
(24-02-2012 05:21 PM)kim Wrote:  I had an entire college course devoted to random probability; the course was called Principles of Mathematics and was only available post college algebra. I loved it so much, I kept the text. It was always beautiful before... but it was in that class when math began to become extremely elegant to me. Heart
Quite probably, one of the first semesters in my life that my favorite class was a math class. Shy

I like math. I still suck at the logic language behind math though. I never had any classes on it though... well, and never really tried to learn it on my own. I can follow most of it as it makes a lot of sense, but can't really put them together properly. In a way, the logic ends up looking the way I write... all over the place. I probably need to spend some time to at least get the basics in. I don't need to, because I don't need it for work or anything, but really should as I go over the stuff all the time.

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27-02-2012, 11:04 AM
RE: Wanna debate a math problem?
(25-02-2012 08:24 AM)craniumonempty Wrote:  
(24-02-2012 05:21 PM)kim Wrote:  I had an entire college course devoted to random probability; the course was called Principles of Mathematics and was only available post college algebra. I loved it so much, I kept the text. It was always beautiful before... but it was in that class when math began to become extremely elegant to me. Heart
Quite probably, one of the first semesters in my life that my favorite class was a math class. Shy

I like math. I still suck at the logic language behind math though. I never had any classes on it though... well, and never really tried to learn it on my own. I can follow most of it as it makes a lot of sense, but can't really put them together properly. In a way, the logic ends up looking the way I write... all over the place. I probably need to spend some time to at least get the basics in. I don't need to, because I don't need it for work or anything, but really should as I go over the stuff all the time.

I too love math but suck at formulas. I'm partial to physics because I find it easier to find practical, real-life applications for it.

“Whenever you find yourself on the side of the majority, it's time to pause and reflect.”

-Mark Twain
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