[Guest]

A man and a woman have two children each. At least one of the woman's children is a boy, and the man's oldest child is a son.

What is the probability that the woman's child not mentioned is a boy? And the man's? Are they even different?

[Guest]

If i have 2 children, what is the probability that they are both boys? By your logic it would be 1/3, but that's clearly not the case. If you say the answer is 1/3 to the question just mentioned, then I'm sorry for you.

By MY logic, the probability would be 1/4, I was using YOUR logic in that statement. My logic states all of the possible combinations. Yours is the one that eliminates the possibility that would make your answer correct.

If you're going to try to argue, please at least read the long other thread first.

Reading a fourteen page thread of people arguing won't change how logic works.

[Guest]

Noct..you r using permutation in probability....I think there is some mistake..or misunderstanding..

1. one is boy...so

2. the other is either boy or girl..so the chance is 1/2..

I know according to the theories of probability, u r correct...but in some cases probability theory does not impress me much...from my high school...upto my postgrad..it sometimes seems very fruitless to me...

[Guest]

Noct..you r using permutation in probability....I think there is some mistake..or misunderstanding..

1. one is boy...so

2. the other is either boy or girl..so the chance is 1/2..

I know according to the theories of probability, u r correct...but in some cases probability theory does not impress me much...from my high school...upto my postgrad..it sometimes seems very fruitless to me...

Which one are you talking about? For the case "at least one child is a boy" it's a 1/3 chance that the other is a boy. For "the oldest is a boy" it's a 1/2 chance the other i a boy.

[Guest]

Guess what? That argument still makes my point...if you're counting both of those as "two boys" then boy/girl and girl/boy are both "one boy, one girl" and therefore, it is still 1/2 probability

Straight from your post.

So if i have two kids all the possibilities are

BB

BG

GB

GG

but according to you BG and GB are the same thing. so: there's a 1/3 chance of having 2 boys, a 1/3 chance of having 2 girls, and a 1/3 chance of having one of each. According to your logic.

[itachi-san]

Noct..you r using permutation in probability....I think there is some mistake..or misunderstanding..

1. one is boy...so

2. the other is either boy or girl..so the chance is 1/2..

I know according to the theories of probability, u r correct...but in some cases probability theory does not impress me much...from my high school...upto my postgrad..it sometimes seems very fruitless to me...

I understand the posts about probability and 1/3 etc..., but I agree with Storm about the logic involved in this particular situation. It shouldn't change the probability if you know that a certain gender is born first because in both cases we know one of the genders.

[Guest]

I understand the posts about probability and 1/3 etc..., but I agree with Storm about the logic involved in this particular situation. It shouldn't change the probability if you know that a certain gender is born first because in both cases we know one of the genders.

But in one of the cases you don't know which child is the boy. And that makes all the difference

[itachi-san]

A man and a woman have two children each. At least one of the woman's children is a boy, and the man's oldest child is a son.

What is the probability that the woman's child not mentioned is a boy? And the man's? Are they even different?

I don't think I'll ever be sold on that Noct. What's the difference between GB and BG in this particular question?

[Guest]

The woman's probability is still 1/2 and here's why:

You know she has a son. Here are the four possibilities:

1. He has an older brother

2. He has a younger brother

3. He has an older sister

4. He has a younger sister

That equals 2/4 or 1/2

Straight from your post.

So if i have two kids all the possibilities are

BB

BG

GB

GG

but according to you BG and GB are the same thing. so: there's a 1/3 chance of having 2 boys, a 1/3 chance of having 2 girls, and a 1/3 chance of having one of each. According to your logic.

I said they are different, I said that following your logic (brother older than the known son and brother younger than the known son being the same) then that would mean that sister older than the known son and sister younger than the known son would be the same. You can't choose to have one be the same and one be different which is what you're trying to do. That is how you are "proving" the probability to be something that it isn't. Everyone knows it is 1/2, because it's obvious, but you're trying to prove that it isn't by choosing which cases to ignore. If you take ALL possible cases, then the probability is 1/2 as stated in my quote above.

Edited March 26, 2008 by GIJeff

[Guest]

I said they are different, I said that following your logic (brother older than the known son and brother younger than the known son being the same) then that would mean that sister older than the known son and sister younger than the known son would be the same. You can't choose to have one be the same and one be different which is what you're trying to do. That is how you are "proving" the probability to be something that it isn't. Everyone knows it is 1/2, because it's obvious, but you're trying to prove that it isn't by choosing which cases to ignore. If you take ALL possible cases, then the probability is 1/2 as stated in my quote above.

Obviously you need to re-think your probability. Because "Everyone" knows it is 1/3. Seriously. Look it up. Go do a statistical analysis on the Census info.

It does matter because it is twice as likely to get BG/GB than BB. I don't understand how you fail to see that...

EDIT:

Take a look here and see if that helps you understand it.

Edited March 26, 2008 by Noct

[Guest]

Obviously you need to re-think your probability. Because "Everyone" knows it is 1/3. Seriously. Look it up. Go do a statistical analysis on the Census info.

It does matter because it is twice as likely to get BG/GB than BB. I don't understand how you fail to see that...

EDIT:

Take a look here and see if that helps you understand it.

It is twice as likely to get BG/GB if you're starting from scratch...if you already have the boy, it is 50/50. It's not rocket science

[Guest]

It is twice as likely to get BG/GB if you're starting from scratch...if you already have the boy, it is 50/50. It's not rocket science

Exactly, it's not rocket science.

It is 50/50 in the case where the older one is a boy. but when we don't know which one is mentioned, there are three possibilities:

BB

BG

GB

and since only one of these is BB, there's a 1/3 chance that the lady has two boys, thus a 1/3 chance that the other child is a boy.

[bonanova]

A valid way to test an hypothesis about probability is to calculate

a sample space and count the favorables. You'd need to be able

to write a simple program and have access to a random number

generator.

Sometimes just translating the conditions of the OP into code,

without even running the code, clarifies things.

I'm very interested to hear some of the claims being made in

this thread tested in this way. Post your results and your code.

Corollary to proof by computer simulation:

Take your theories of probability to Las Vegas.

The credence of your theory stands in direct correlation to the length of time that your net worth increases.

[Guest]

Noct..you r using permutation in probability....I think there is some mistake..or misunderstanding..

1. one is boy...so

2. the other is either boy or girl..so the chance is 1/2..

I know according to the theories of probability, u r correct...but in some cases probability theory does not impress me much...from my high school...upto my postgrad..it sometimes seems very fruitless to me...

Please see my previous post for why your conclusion #2 is flawed. The explanation to my fourth proposed question explained why. You may know the gender of the other child, but you don't know which child that is. Therefore, when you refer to the other, you still don't know which one you're referring to, so you can't treat it as though it's an independent probability.

[itachi-san]

It doesn't matter which child it is. Having a child is an independent action. There is no implied questioning like: if a couple is starting from scratch, what will the probability be, etc... As for the link to the HS girl's example, that really wasn't very impressive evidence. I will only believe this being 1/3 if someone can do what bonanova has requested and make a program. My answer is 1/2 unless I see that it is not via some kind of substitution example. Also, text books have been proven wrong plenty of times which is why they have multiple editions, so I'm not going to say: "oh, some random girl's High School Math Textbook says it's 1/3 so that must be the answer."...

[Guest]

It doesn't matter which child it is. Having a child is an independent action. There is no implied questioning like: if a couple is starting from scratch, what will the probability be, etc... As for the link to the HS girl's example, that really wasn't very impressive evidence. I will only believe this being 1/3 if someone can do what bonanova has requested and make a program. My answer is 1/2 unless I see that it is not via some kind of substitution example. Also, text books have been proven wrong plenty of times which is why they have multiple editions, so I'm not going to say: "oh, some random girl's High School Math Textbook says it's 1/3 so that must be the answer."...

We are not saying the chances of having a boy or a girl are affected at all. But the chance of having two boys given at least one child is a boy is 1/3. If you have 1 boy and are having another child, it is ~1/2 to have a boy/girl. But the conditional probability is affected.

[Guest]

It doesn't matter which child it is. Having a child is an independent action. There is no implied questioning like: if a couple is starting from scratch, what will the probability be, etc... As for the link to the HS girl's example, that really wasn't very impressive evidence. I will only believe this being 1/3 if someone can do what bonanova has requested and make a program. My answer is 1/2 unless I see that it is not via some kind of substitution example. Also, text books have been proven wrong plenty of times which is why they have multiple editions, so I'm not going to say: "oh, some random girl's High School Math Textbook says it's 1/3 so that must be the answer."...

I'm not sure where you're seeing a high school girl's textbook. Is it on a previous page?

Also, a quick temporary substitution for a program: flip two coins. Chart the times you have 2 heads out of the times you have at least one head.

Sorry for double post!

EDIT:

Here's something I found:

"Quite a lot of people refuse to believe this because they think that if a man has two children, he can have two boys, two girls or one of each, i.e., three possibilities, each equally likely. But they're not equally likely, because 'one of each' is not one possibility, but two. Think of all the people you know with 2 children, and you'll find that roughly a quarter of them have two boys, a quarter have two girls, and half of them have one of each."

Edited March 26, 2008 by Noct

[Guest]

I flipped two U.S. Quarters in a row, 200 times (400 flips total). I came up with the following distribution:

TT-57

HT/TH-97

HH-46

So we can see that at least one head occurred 143 times. Out of that, 46 of them were HH. This leaves us with the fact that out of the times at least one flip was head, 32.2% of the time the other flip was heads as well (46 out of 143).

I don't know about you, but for me that's close enough to 1/3 to call it confirmed. First in theory, now in application.

For you naysayers who don't believe me or think I lied or cheated, go do it yourself.

Edited March 26, 2008 by Noct

[Guest]

It doesn't matter which child it is. Having a child is an independent action. There is no implied questioning like: if a couple is starting from scratch, what will the probability be, etc...

But there is an implied question in the OP, which is what I tried to point out earlier. The question is: which child are you talking about? You are right that "having a child is an independent action," but in the case of the woman's two children, it's not just a question of whether or not a particular child is likely to be a boy. Try to understand the difference between:

1. A woman has a boy, and she is about to have another child. What is the probability that the new child will be a boy? What are the odds that she will have two boys? Both questions are the same, and the answer is clearly 50%

2. A woman has two children, one of whom is a boy. What is the probability that the other is a boy? What is the probability that they are both boys? If you think about it, you will understand that once again, both questions are the same. You have to use the same approach involving a delineation of the possible outcomes (BB,BG,GB) in order to arrive at an answer.

[Guest]

well folks, when bonanova has some help from ERNIE and your done with the probability thing - maybe never. How about looking at bioligy, then family history, and a few other gambits - through to sun spots (yes sun spots)

My mum had six children BGBGBG maybe some ambiguous parenthood if i am being honest.

The offspring of these were

B = G

G = GG

B = 0 (seedless)

G = B

B = GGBG (me)

G = BB

birth order there was GGGGGGBBBGB

Play with those or look at your own family, but this is not a game for stratergy, more biological i think.

If you wish use the info - ask for more details too, I don't mind.

Incest - a game the whole family can play!

[Guest]

well folks, when bonanova has some help from ERNIE and your done with the probability thing - maybe never. How about looking at bioligy, then family history, and a few other gambits - through to sun spots (yes sun spots)

My mum had six children BGBGBG maybe some ambiguous parenthood if i am being honest.

The offspring of these were

B = G

G = GG

B = 0 (seedless)

G = B

B = GGBG (me)

G = BB

birth order there was GGGGGGBBBGB

Play with those or look at your own family, but this is not a game for stratergy, more biological i think.

If you wish use the info - ask for more details too, I don't mind.

Incest - a game the whole family can play!

It's completely possible that genetics could have some play in this. I don't know too much about them so I won't say how they affect anything.

In the puzzle, we're talking about a theoretical situation, so genetic anomalies wouldn't matter.

But back to your comment. It's still possible that with the ~50 percent chance of gender, you could still end up with your situation. If i flipped a coin twice and got heads twice, would you call foul play? No of course not. If i flipped it 10 times and got 9 heads, is that foul play? There's a possibility, but it's still easily inside the realm of probability. I think from the short excerpt of your family history that your genes still fall well within the standard deviations of the norm ~50%. If you can trace back further and show a streak of 50-100 girls in a row, then that is something that is more likely not up to the percentages predicted. But as for now, I think your family still qualifies well within the acceptable numbers, based on what's given.

Edited March 26, 2008 by Noct

[Guest]

Well coin flipping is also subjest to other influences, but these can be controlled, Biological matters are very difficult to control. (perhaps we should flip some willing maids onto their back and see if any random/predictable births ensue). This is somewhat random and not predictable, perhaps we get further along that route in the distant future if science allows, maths is ready maybe, bioligy is not.

It is probably interesting to view figures of various indiginous populations and also viewing the random factors. If you look at the effect of Vietnam war that produced a few random births caused by outside influences - from rape to who knows what- survival/love or fatal attraction).

Seperately look at a new suitor male lion who deposes he origianl king then kills the young of that king and imediately mates with the willing female of that king starting a new generation. Something to do with the survival of the fittest theory but also a variation bought in that MUST be viewed in the long term/history equation. what does math make of this. It is more animalistic rather than choices influenced by our modern and moral values.

Somethings just are not all maths, though it's part of predicting and experimentation (controlled with predictive results, not just for experiments sake) I am willing to be part of the experiment historically or otherwise - bring on the dancing girls, leave out the clowns.

Sorry if this is off at a tangent to the other posts, but it does not seem to be considered at all - maybe some think it should'nt - they can tell me so or take it through another thead/topic. Perhaps it has too many variables.

[Guest]

Well coin flipping is also subjest to other influences, but these can be controlled, Biological matters are very difficult to control. (perhaps we should flip some willing maids onto their back and see if any random/predictable births ensue). This is somewhat random and not predictable, perhaps we get further along that route in the distant future if science allows, maths is ready maybe, bioligy is not.

It is probably interesting to view figures of various indiginous populations and also viewing the random factors. If you look at the effect of Vietnam war that produced a few random births caused by outside influences - from rape to who knows what- survival/love or fatal attraction).

Seperately look at a new suitor male lion who deposes he origianl king then kills the young of that king and imediately mates with the willing female of that king starting a new generation. Something to do with the survival of the fittest theory but also a variation bought in that MUST be viewed in the long term/history equation. what does math make of this. It is more animalistic rather than choices influenced by our modern and moral values.

Somethings just are not all maths, though it's part of predicting and experimentation (controlled with predictive results, not just for experiments sake) I am willing to be part of the experiment historically or otherwise - bring on the dancing girls, leave out the clowns.

Sorry if this is off at a tangent to the other posts, but it does not seem to be considered at all - maybe some think it should'nt - they can tell me so or take it through another thead/topic. Perhaps it has too many variables.

But random births/survival of the fittest etc. should all still not affect the male/female ratio. I understand what you're saying about the indigenous populations, but I don't understand the application you make with the lion or Vietnam examples.

Edited March 26, 2008 by Noct

[Guest]

Flipping coins doesn't convince me. You're doing an experiment in which one of the possible outcomes is that she has 2 girls. Within the confines of this puzzle, that is not possible. Let me use a real world scenario:

You overhear a woman having a conversation. During this conversation, you hear her mention that she has two children. Later in the conversation she mentions her son.

There are two possibilities:

1) She was talking about her oldest child, and there is a 50/50 chance that her younger child is also a son.

2) She was talking about her youngest child, and there is a 50/50 chance that her older child is also a son.

How in the world do you put those two together and somehow decide that there is only a 33% chance that her other child is a son?

[bonanova]

Flipping coins doesn't convince me. You're doing an experiment in which one of the possible outcomes is that she has 2 girls. Within the confines of this puzzle, that is not possible. Let me use a real world scenario:

You overhear a woman having a conversation. During this conversation, you hear her mention that she has two children. Later in the conversation she mentions her son.

There are two possibilities:

1) She was talking about her oldest child, and there is a 50/50 chance that her younger child is also a son.

2) She was talking about her youngest child, and there is a 50/50 chance that her older child is also a son.

How in the world do you put those two together and somehow decide that there is only a 33% chance that her other child is a son?

Using that approach, you come up with the result that of the population

of families with two children, at least one of which is a boy, [only] half

of them have one boy and one girl.

Are you comfortable with that result?

[Guest]

Using that approach, you come up with the result that of the population of families with two children, at least one of which is a boy, half of them have one boy and one girl.

Are you comfortable with that result?

Are you comfortable with saying that EXACTLY one third have two boys, and EXACTLY two thirds have one boy and one girl? I didn't think so. We're talking probability, which is math, so I'm just trying to figure out how the math works for it.