[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?

[bonanova]

I'm just trying to figure out how the math works for it.

Here's a hint.

With the assumption of equal probability of boy/girl at each birth,

families with two children will have opposite gender children half the time

and same gender children half the time. [boys 1/4 and girls 1/4].

That should help you with the math.

[Guest]

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.

It's not yet fully understood by anyone - yet! Observations are being made, results are investigated and the assesments are forever developing. Which is partly my point regarding maths is avaiable but bioligy and outside influences effect the results, global warming too will probably have a degree of implicating negative/positive results.

My main point is we are a developing society trying to make choices that in this case probaly does not concur with rationality/chances/probability. The lion situation is not so far removed from humans, King Herod, most egyptian/roman pious attitudes regarding domination and control.

regarding math, the puzzle as it stands. 50/50 (subject to bioligical influences and human nature being a strange beast to say the least)

[Guest]

Surely its 1 in 2

[Guest]

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.

We never said EXACTLY two thirds have one boy and one girl and EXACTLY one third have two boys (out of those that have at least one boy). This is not how probability works. Surely you understand that. If I flip a coin twice, will you tell me that EXACTLY 1 time will be head and EXACTLY 1 time will be tails? Of course not.

We're not saying exactly, we're talking about the probabilities. It's twice as likely that the woman's child not mentioned is a girl than it is a boy. But we can't say it'll exactly happen that way.

[Guest]

Heres the problem. You seem to think that the order of the siblings affects the probability. It does not.

But lets pretend age does matter for a moment.

Lets say you know the eldest child is a boy. What are the odds that his younger sibling is also a boy? By your own admission it is 1/2.

Now lets say that the youngest child is a boy. What are the odds that his older sibling is a also a boy? The same 1/2.

Either branch you take the odds are the same 1/2.

Let me restate the problem using quarters. Lets say heads for boys and tails for girls.

Take one quarter and put it heads up to represent the one boy you already know.

Now flip the other one a fair number of times and average your results. You will probably come close to 1/2.

[Guest]

Heres the problem. You seem to think that the order of the siblings affects the probability. It does not.

But lets pretend age does matter for a moment.

Lets say you know the eldest child is a boy. What are the odds that his younger sibling is also a boy? By your own admission it is 1/2.

Now lets say that the youngest child is a boy. What are the odds that his older sibling is a also a boy? The same 1/2.

Either branch you take the odds are the same 1/2.

Let me restate the problem using quarters. Lets say heads for boys and tails for girls.

Take one quarter and put it heads up to represent the one boy you already know.

Now flip the other one a fair number of times and average your results. You will probably come close to 1/2.

This is true when we know the oldest is a boy. In the case of the woman, we don't know which child is a boy, so this affects the probability. There is a 1/3 chance there are two boys when we don't know which one is already a boy.

[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?

Are they even different? -What does this mean ?

Either way the gender of unknown are 50/50?

Seems a lot of input (which is great to encourage) but it is going nowhere and probability has been done to death.

Let's hear something inciteful pleeeeeeeease!

[Guest]

Are they even different? -What does this mean ?

Either way the gender of unknown are 50/50?

Seems a lot of input (which is great to encourage) but it is going nowhere and probability has been done to death.

Let's hear something inciteful pleeeeeeeease!

"Are the even different" was referring to the chances of the other child being a boy for the man and woman. Yes they are different because the man's chance is 1/2, while the woman's chance is 1/3. It is twice as likely that the woman's other child is a girl than a boy, yet the man's chances are even.

[Guest]

You made a mistake. Bb and bB are the same thing aren't they? That should change your answers to the correct ones

Bb and bB are NOT the same thing. I have a twin brother, and believe me, birth order is important.

Just knowing you have a boy doesn't change the probability, because you don't know the birth order.

Lets say we have two coins, a penny and a dime. You flip the coins, and I tell you that you have a head. What is the probability that the other is a head as well?

Say capitol is head, lower case is tail: possibilities Pd, PD, pD, so the probability is 1/3.

Now, say we have two pennies: Possibilities Pp PP, probability is 1/2.

The problem is in how you state the relationship. If I know the difference in the two, like it is the oldest boy that is known, then we have pennies and dimes. If I don't then I have two pennies, and can't tell the difference.

Just saying you have at least one boy doesn't say whether there is a difference in age. You can't go to the BB,GB,BG,GG because that is just having two children, we have placed a condition that we have a boy. That boy can be an older boy, or a younger boy with equal probability according to the problem. The sibling can be an older boy or younger boy, and older sister or younger sister, so the probability of having another boy is 1/2.

Like I said in my earlier post, if there was a qualifier that the boy was the oldest boy, or youngest boy, then that would change the probability to 1/3, but because we don't know that, the probability is still 1/2.

[Guest]

Bb and bB are NOT the same thing. I have a twin brother, and believe me, birth order is important.

Just knowing you have a boy doesn't change the probability, because you don't know the birth order.

Lets say we have two coins, a penny and a dime. You flip the coins, and I tell you that you have a head. What is the probability that the other is a head as well?

Say capitol is head, lower case is tail: possibilities Pd, PD, pD, so the probability is 1/3.

Now, say we have two pennies: Possibilities Pp PP, probability is 1/2.

You keep changing your posting methods. So if we want to talk about order, are you saying PD and DP are not the same thing? The capitals don't matter to the Bb bB. So you're saying that having an oldest boy first, and a younger boy second is different than having a younger boy second and an older boy first? I think you missed what you were saying before. if one is a head(boy) it doesn't matter what kind of order you put it in, the other one will be a head(boy) or not. So you're saying pd and dp are different?

The problem is in how you state the relationship. If I know the difference in the two, like it is the oldest boy that is known, then we have pennies and dimes. If I don't then I have two pennies, and can't tell the difference.

Just saying you have at least one boy doesn't say whether there is a difference in age. You can't go to the BB,GB,BG,GG because that is just having two children, we have placed a condition that we have a boy. That boy can be an older boy, or a younger boy with equal probability according to the problem.

Exactly, so that's why if we list the first born first, there are three possibilities.

BB

BG

GB

these are the only ways you can have two children and at least one of them is a boy. Only one of these is a case where the other child is also a boy, so there is a 1/3 chance that the other child is a boy.

Like I said in my earlier post, if there was a qualifier that the boy was the oldest boy, or youngest boy, then that would change the probability to 1/3, but because we don't know that, the probability is still 1/2.

You have your logic backwards. If we know whether the boy is older/younger, than the chance is 1/2 that the other child is a boy. If we don't know which one it is, there's a 1/3 chance the other child is a boy.

[Guest]

"Are the even different" was referring to the chances of the other child being a boy for the man and woman.

Yes they are different because the man's chance is 1/2,

while the woman's chance is 1/3.

It is twice as likely that the woman's other child is a girl than a boy, yet the man's chances are even.

Thanks for that but...

For some reason (it happens too often), I don't see the logic/probability/math etc.

Best not to try and ram it home - I become closed minded in these situations, if it is as you say then fine and well done - most people will just want healthy children no matter what the sex.

My first had a foot pointing the wrong way - you would'nt know it now. besides she walked at 10/12, ran over a springy bed at 11/12 and climbed out of her cot at 1 - super happy great lovely and fantastic too. .. She works in payroll and is rubbish at math.

[Guest]

Thanks for that but...

For some reason (it happens too often), I don't see the logic/probability/math etc.

Best not to try and ram it home - I become closed minded in these situations, if it is as you say then fine and well done - most people will just want healthy children no matter what the sex.

My first had a foot pointing the wrong way - you would'nt know it now. besides she walked at 10/12, ran over a springy bed at 11/12 and climbed out of her cot at 1 - super happy great lovely and fantastic too. .. She works in payroll and is rubbish at math.

Fair enough

I'd be the same way if you tried to explain some microbiology to me or other subjects

[Guest]

Let me restate the problem using quarters. Lets say heads for boys and tails for girls.

Take one quarter and put it heads up to represent the one boy you already know.

Now flip the other one a fair number of times and average your results. You will probably come close to 1/2.

In your case, you already know which quarter is the heads, so it's not the same. Let's modify your test a bit ...

Flip two quarters, and cover them both. Reveal one. If it is heads, reveal the other, and track the ratio of heads to tails for the second quarter. If it is tails, ignore it and flip again. I am pretty sure that you will find after enough tries that when you reveal the second quarter, it will be heads 1 out of 3 times.

[Guest]

Not quite. the order doesn't matter in the sense of we didn't specify the order, but it does effect the probability.

Sorry Noct,I don't understand what you wanna say.If it is that,if you have 2 children thair gender effect the probability what will be the sex of the next child,you are totaly wrong.As I said before the chances to have boy/girl are ALWEYS 1/2 NO MATTER WHAT.I don't believe how you people can continue with such nonsenses.

[Guest]

You have your logic backwards. If we know whether the boy is older/younger, than the chance is 1/2 that the other child is a boy. If we don't know which one it is, there's a 1/3 chance the other child is a boy.

I know that statement isn't directed at me, but YOU are the one who has the logic messed up. You are saying that birth order matters for BG/GB but not for BB. You can't pick and choose when it matters in logic. Mathematically, yes, there's twice the chance to have a BG, than BB, but LOGICALLY, there is the same chance.

if one is a head(boy) it doesn't matter what kind of order you put it in, the other one will be a head(boy) or not.

That argument works against you. That says that BG and GB are the same which you are saying isn't.

[bonanova]

Sorry Noct,I don't understand what you wanna say.If it is that,if you have 2 children thair gender effect the probability what will be the sex of the next child,you are totaly wrong.As I said before the chances to have boy/girl are ALWEYS 1/2 NO MATTER WHAT.I don't believe how you people can continue with such nonsenses.

Hi ash013,

Try thinking of it this way.

For families with two children, opposite genders occur half the time.

But two boys happen only 1/4 of the time, and two girls happen 1/4 of the time.

So the odds of two boys can never be the same as the odds of one boy and one girl.

Do you see how that is different from just asking the gender of one particular child?

[Guest]

I know that statement isn't directed at me, but YOU are the one who has the logic messed up. You are saying that birth order matters for BG/GB but not for BB. You can't pick and choose when it matters in logic. Mathematically, yes, there's twice the chance to have a BG, than BB, but LOGICALLY, there is the same chance.

That argument works against you. That says that BG and GB are the same which you are saying isn't.

There is only one way to get BB, so it is twice as likely to get BG/GB than it is to get BB. I don't understand how you say mathematically there's twice the chance but logically they are the same? I don't understand how you're saying there is any sort of birth order in BB. Either you have a girl then a boy, or a boy then a girl, but there is only 1 order that can happen with BB. You have a boy, then a boy, so there are no order variations on that.

The second comment you quoted doesn't work against me. I didn't say that the probability was even, but just that when one of them is heads (we don't know which one) the other one will be either heads or tails (which hopefully we all already knew)

[Guest]

Sorry Noct,I don't understand what you wanna say.If it is that,if you have 2 children thair gender effect the probability what will be the sex of the next child,you are totaly wrong.As I said before the chances to have boy/girl are ALWEYS 1/2 NO MATTER WHAT.I don't believe how you people can continue with such nonsenses.

We are stressing that it does NOT effect the probability of having a boy or a girl. If that is how you are interpreting it, then you are correct that it will be ~50% for the population.

[Guest]

I think that they are both married, meaning the probability of the unmentioned child being a boy is 100%. Notice how the riddle says his oldest son. If they had a boy and a girl, it would be the oldest child, wouldn't it?

[Guest]

I think that they are both married, meaning the probability of the unmentioned child being a boy is 100%. Notice how the riddle says his oldest son. If they had a boy and a girl, it would be the oldest child, wouldn't it?

Yea sorry about the question not being clear. I tried to clear it up in post 3, but most people only read the first post when they try to answer the puzzle. They aren't related at all and have never met before etc.

[bonanova]

Here's a puzzle that most of can't solve.

Only the ones who know how to defend the 1/2 answer can solve it.

Puzzle.

A family has two children.

Assume each child had a 50/50 chance at birth of being a boy.

State the conditions under which it is equally likely that the children are (a) both boys and (b) mixed gender.