Math/logic question #2

[jwvdcw]

A family has two children. One of them is male. What is the chance that the other one is also male?

[Utah]

What am I missing here?

The odds of the other child being male is 50% (assuming that the likelihood of male/female is 50/50).

The chances of a child being male not affected by the sex of the other child (barring some biological reasons).

Its like saying, I flipped a coin twice and the first one was tails. What was the likelihood the second one was tails? Obviously 50/50.

people make this mistake in chance games all the time. They believe that the results of previous random events has an affect of future unconnected random events.

I think I am missing something to your question.

[jwvdcw]

Utah, you are incorrect.

[La Brujita]

This to me is a question of English rather than logic.

Is the original statement to be understood at least one is male, or to be read in the following way:

my buddy has two kids one is a boy named carson and the other just came out yesterday. Then its 50/50

Edit to say I am confusing myself a bit so I will think about it.

[BeerMoney]

It really should say, "It is known that one is a boy, what are the chances both are boys.." The way you wrote the question, Prob=.5

Sample space for two kids {BB, BG, GB, GG}

If you say, it is known that one is a boy, what are the chances both are boys, we eliminate GG, and and now the chances are 2/3.. Like someone else posted, its more of a grammer thing than anything.

[Kurn, son of Mogh]

The odds of the other child being male is 50%

This is actually not true. I believe the probability that a child will be male is closer to 51%

[jwvdcw]

[ QUOTE ]
It really should say, "It is known that one is a boy, what are the chances both are boys.." The way you wrote the question, Prob=.5

Sample space for two kids {BB, BG, GB, GG}

If you say, it is known that one is a boy, what are the chances both are boys, we eliminate GG, and and now the chances are 2/3.. Like someone else posted, its more of a grammer thing than anything.

[/ QUOTE ]

You are correct in your answer. But I think I wrote the question just fine. "One of them is male" is not equivalent to "It is known that one is a boy" to you? It sure is to me.

[jwvdcw]

The answer is: The chances are 33% that the other one is a male.

Here are the possible combinations:

BB
BG
GB
GG

Where one of them is male, the other one is male 33% of the time.

[Stu Pidasso]

[ QUOTE ]
Here are the possible combinations:
BB
BG
GB
GG


[/ QUOTE ]

BG and GB are equivilents, therefore its a 50% chance.

Stu

[Utah]

Sorry, my answer is correct given the way you wrote the question.

"What is the chance that the other one is also male?"
Its always 50/50 that either child is male.

Now, if you answered the question correctly for the answer your getting at:

"What is the chance that a household has two boys if you know that they didnt have two girls"

Then I believe you are correct in 33%

[jwvdcw]

[ QUOTE ]
[ QUOTE ]
Here are the possible combinations:
BB
BG
GB
GG


[/ QUOTE ]

BG and GB are equivilents, therefore its a 50% chance.

Stu

[/ QUOTE ]

No they are not. Lets say you have two kids. One is older and one is younger(obviously).

The older is a girl; The younger one is a boy.
The older one is a boy; The younger one is a girl.

Those are different.

[jwvdcw]

[ QUOTE ]
Sorry, my answer is correct given the way you wrote the question.

"What is the chance that the other one is also male?"
Its always 50/50 that either child is male.


[/ QUOTE ]

You are correct, it is always 50% that any one child is male. But if I tell you that one child is male(and I don't specify which one) what are the odds that the other one is also male, then its 33%.

[jwvdcw]

1.Kid A=male, Kid B=male
2.Kid A=male, Kid B=female
3.Kid A=female, Kid B=male
4.Kid A=female, Kid B=female

If one is male, what are the chances that the other one is male?

Ok, to start off we have to eliminate cases that don't fit the antecedant. Therefore, we must eliminate all cases where one isn't male. Therefore, we eliminate case 4.

That leaves us with 3 choices: 1,2, and 3. Out of those 3, in only one of them is the other kid male. 1/3=33%.

[jwvdcw]

[ QUOTE ]
It really should say, "It is known that one is a boy, what are the chances both are boys.." The way you wrote the question, Prob=.5

Sample space for two kids {BB, BG, GB, GG}

If you say, it is known that one is a boy, what are the chances both are boys, we eliminate GG, and and now the chances are 2/3.. Like someone else posted, its more of a grammer thing than anything.

[/ QUOTE ]

You have the right idea, but I think you meant to type 1/3 instead of 2/3.

[Stu Pidasso]

[ QUOTE ]
1.Kid A=male, Kid B=male
2.Kid A=male, Kid B=female
3.Kid A=female, Kid B=male
4.Kid A=female, Kid B=female

If one is male, what are the chances that the other one is male?

Ok, to start off we have to eliminate cases that don't fit the antecedant. Therefore, we must eliminate all cases where one isn't male. Therefore, we eliminate case 4.

That leaves us with 3 choices: 1,2, and 3. Out of those 3, in only one of them is the other kid male. 1/3=33%.


[/ QUOTE ]

How is case 2 different from case 3? In the context of your original antecedant, they appear to be the same. Instead of having 3 choices in reality you only have 2 choices.

Stu

[jwvdcw]

[ QUOTE ]
[ QUOTE ]
1.Kid A=male, Kid B=male
2.Kid A=male, Kid B=female
3.Kid A=female, Kid B=male
4.Kid A=female, Kid B=female

If one is male, what are the chances that the other one is male?

Ok, to start off we have to eliminate cases that don't fit the antecedant. Therefore, we must eliminate all cases where one isn't male. Therefore, we eliminate case 4.

That leaves us with 3 choices: 1,2, and 3. Out of those 3, in only one of them is the other kid male. 1/3=33%.


[/ QUOTE ]

How is case 2 different from case 3? In the context of your original antecedant, they appear to be the same. Instead of having 3 choices in reality you only have 2 choices.

Stu

[/ QUOTE ]

Because they're two different kids! Call them kid #1 and kid #2 or Kid A and Kid B or whatever you want. They can go G-B or B-G.

[jwvdcw]

Ok, here let me try to illustrate this way. Suppose I have two kids. One is named Mike and one is Steve. They both like to dye their hair different colors. Their favorite colors to dye their hair are black and blonde. At different times throughout the year, I plan to check up on them to see what color their hair is. Can you agree with me that there are 4 possible combonations that their hair might be whenever I check up on them??

1.Mike-blonde, Steve-blonde
2.Mike-blonde, Steve-black
3.Mike-black, Steve-blonde
4.Mike-black, Steve-black

do you see how 2 and 3 are different?

[jwvdcw]

Every single person seems to disagree with me here, so hopefully I'll have a lot of takers on this bet:

I will pay for your airfair to meet me whenever you have time.


We will flip two coins together. Whenever one of these coin flips is a head, our bet will be on. If the other coin is also a head, then you win, if the other coin is a tail, then I win. If you say this is 50/50, then you will love this next part: I will offer you 1.5-1 odds, meaning that if you put up $100, I'll put up $150. We will do this all day long.

I am completely serious about this and willing to pay for your airfare, hotel accomodations, and even buy your food while you're out here. I only ask that we do this bet a large number of times so that short-term luck doesn't come into play.

PM me if interested. Serious inquiries only.

[daryn]

how silly is this?

you think that somehow the flip of your coin affects the flip of another coin? this is not the EPR paradox, it's flipping coins. the fact that YOUR coin is heads or tails doesn't affect the other coin.



edit: oops, i thought you were saying something different. like.. if YOUR coin was heads, the game is on. you said "if either was heads".

in short, nevermind

[Homer]

1/3, right?

[jwvdcw]

[ QUOTE ]
1/3, right?

[/ QUOTE ]

first person to get it right I think

[jwvdcw]

[ QUOTE ]
Every single person seems to disagree with me here, so hopefully I'll have a lot of takers on this bet:

I will pay for your airfair to meet me whenever you have time.


We will flip two coins together. Whenever one of these coin flips is a head, our bet will be on. If the other coin is also a head, then you win, if the other coin is a tail, then I win. If you say this is 50/50, then you will love this next part: I will offer you 1.5-1 odds, meaning that if you put up $100, I'll put up $150. We will do this all day long.

I am completely serious about this and willing to pay for your airfare, hotel accomodations, and even buy your food while you're out here. I only ask that we do this bet a large number of times so that short-term luck doesn't come into play.

PM me if interested. Serious inquiries only.

[/ QUOTE ]

What happened to everyone who was saying that I was so wrong?? /images/graemlins/wink.gif

[kyro]

It IS 1/3, but the answer is tricky and unfair and I hate you tricky and unfair answer... However, I do like the coin comparison. You could probably make a bundle off it.

[moondogg]

To you they may be different, but to me (and the rest of the world), it makes absolutely no difference which is which. If you had defined in your original question that the order was important, it would have an impact, but you didn't, so it doesn't. I doesn't matter what color there hair is or how old they are or how tall they are or whether they will be raised Christian, Jew, or miscellaneous.

[ QUOTE ]
A family has two children. One of them is male. What is the chance that the other one is also male?


[/ QUOTE ]

You've nailed one of them as male. Good for him, but I really don't care about him. He tells me nothing. Take him away. Lock him in a closet. Bury him in the back yard for all I care. Here's the thing: he is not a variable, and he cannot tell me anything about the other child. Therefore, he is useless to me. He is a red herring, and should be overlooked at worst, and completely removed at best. That leaves one child that is unknown. %50/%50 (or, %51/%49, depending on how picky you will be).

Here's you're sample set: 2 boys, one of each, or 2 girls.
1 boy and 1 girl is no different than 1 girl and 1 boy. %50/%50. If the order matters, you are asking a different question. What is the chance that the other is male? Well, in that case you are definitely talking about the OTHER one, not the original one you defined to be a male. This whole idea of their being two children and either one may or may not be male given that at least one or the other is male is logical slight of hand; you are completely redefining the question, and that redefinition yields a different answer. If go back the the original question you asked, the answer is %50/%50. If you want to answer to be 2/3, ask a different question.

[pudley4]

Let's look at the set of all families who have exactly 2 children. It's pretty safe to say that they will break down approximately this way:

25% have 2 boys
50% have 1 boy, 1 girl
25% have 2 girls.

Now, out of that entire set of families, we choose exactly one. This family has one child who is a boy. What is the probability that the second is also a boy?

It seems pretty obvious that it would be 1/3.

[jwvdcw]

[ QUOTE ]


[ QUOTE ]
A family has two children. One of them is male. What is the chance that the other one is also male?


[/ QUOTE ]

You've nailed one of them as male. Good for him, but I really don't care about him. He tells me nothing. Take him away. Lock him in a closet. Bury him in the back yard for all I care. Here's the thing: he is not a variable, and he cannot tell me anything about the other child. Therefore, he is useless to me. He is a red herring, and should be overlooked at worst, and completely removed at best. That leaves one child that is unknown. %50/%50 (or, %51/%49, depending on how picky you will be).


[/ QUOTE ]

But thats the thing. I didn't say, "One is male, what are the odds the other one is male." In that case, it would be 50/50.

I used the word 'IF'. That changes everything because then it is no longer telling you that one is male and asking about the other one, it is telling you that ONE OF THEM(but not telling you which one) is male. Theres a huge difference.

[jwvdcw]

[ QUOTE ]

Here's you're sample set: 2 boys, one of each, or 2 girls.
1 boy and 1 girl is no different than 1 girl and 1 boy. %50/%50. If the order matters, you are asking a different question. What is the chance that the other is male? Well, in that case you are definitely talking about the OTHER one, not the original one you defined to be a male. This whole idea of their being two children and either one may or may not be male given that at least one or the other is male is logical slight of hand; you are completely redefining the question, and that redefinition yields a different answer. If go back the the original question you asked, the answer is %50/%50. If you want to answer to be 2/3, ask a different question.

[/ QUOTE ]

I honestly can't believe that so many people can't see that G-B and B-G are two different possibilities, but here, I think this will prove it to everybody(and if you still don't believe me, then why not take me up on my bet??):

What are the odds that if a family has 2 kids that both are boys? The answer is 25%. Hopefully, you don't need the math spelled out for you here.

What are the odds that both are girls...25%

The only other choice left is one boy and one girl. And since 25%+25%= only 50% that means that 50% falls into that last category of one boy and one girl.

So fine, if you really want to say that B-G and G-B are the same, then go ahead. But as you can see by the math above, that choice is twice as likely as either of the other choices!

So fines, lets then do it like this:

BB(.25)
GG(.25)
BG(.50)

Going back to the original problem, we can eliminate GG because at least one of them isn't a boy. Therefore we are left with BG(.5) and BB(.25). As you can see, the 'other' kid is a girl twice as often as its a boy(.5 is 2x .25). Another way to phrase twice as likely is 66%-33%.

This really is silly as G-B and B-G are indeed separate choices, but fine do it this way.

[jwvdcw]

[ QUOTE ]
Let's look at the set of all families who have exactly 2 children. It's pretty safe to say that they will break down approximately this way:

25% have 2 boys
50% have 1 boy, 1 girl
25% have 2 girls.

Now, out of that entire set of families, we choose exactly one. This family has one child who is a boy. What is the probability that the second is also a boy?

It seems pretty obvious that it would be 1/3.

[/ QUOTE ]

Thank you for getting it. I can't believe people honestly are trying to tell me that B-G and G-B are the same...do they really think that the odds of having two boys are the same as having one boy and one girl???

[moondogg]

[ QUOTE ]
But thats the thing. I didn't say, "One is male, what are the odds the other one is male." In that case, it would be 50/50.


[/ QUOTE ]

Actually, that IS what you said. They original question was:
[ QUOTE ]

A family has two children. One of them is male. What is the chance that the other one is also male?


[/ QUOTE ]

[ QUOTE ]

I used the word 'IF'.


[/ QUOTE ]

No you didn't.


[ QUOTE ]
That changes everything because then it is no longer telling you that one is male and asking about the other one, it is telling you that ONE OF THEM(but not telling you which one) is male. Theres a huge difference.


[/ QUOTE ]

That's why it is a different question.

[jwvdcw]

[ QUOTE ]
[ QUOTE ]
But thats the thing. I didn't say, "One is male, what are the odds the other one is male." In that case, it would be 50/50.


[/ QUOTE ]

Actually, that IS what you said. They original question was:
[ QUOTE ]

A family has two children. One of them is male. What is the chance that the other one is also male?


[/ QUOTE ]

[ QUOTE ]

I used the word 'IF'.


[/ QUOTE ]

No you didn't.


[ QUOTE ]
That changes everything because then it is no longer telling you that one is male and asking about the other one, it is telling you that ONE OF THEM(but not telling you which one) is male. Theres a huge difference.


[/ QUOTE ]

That's why it is a different question.

[/ QUOTE ]

my fault, you're right.

Here is why you can't 'Take him away. Lock him in a closet. Bury him in the back yard for all I care.'

I said, "one of them is male." I didn't tell you which one. So you can't just throw him away.

Bottom line: On average, a 2 kid family where one of them is male...the other one will be male 33% of the time.

[jwvdcw]

[ QUOTE ]
It IS 1/3, but the answer is tricky and unfair and I hate you tricky and unfair answer... However, I do like the coin comparison. You could probably make a bundle off it.

[/ QUOTE ]

I'm still eagerly waiting for somebody to take me up on that....please I'm begging you!

Let me reassure you once again...I am totally serious about that. PM me if interested.

[moondogg]

[ QUOTE ]
I honestly can't believe that so many people can't see that G-B and B-G are two different possibilities, but here, I think this will prove it to everybody(and if you still don't believe me, then why not take me up on my bet??):


[/ QUOTE ]
Because, despite spending a few minutes here and there discussing it, I have better things to do with my time than hang out with you.

[ QUOTE ]

What are the odds that if a family has 2 kids that both are boys? The answer is 25%. Hopefully, you don't need the math spelled out for you here.


[/ QUOTE ]
Fine.

[ QUOTE ]

What are the odds that both are girls...25%


[/ QUOTE ]
Fine.

[ QUOTE ]

The only other choice left is one boy and one girl. And since 25%+25%= only 50% that means that 50% falls into that last category of one boy and one girl.


[/ QUOTE ]
You're starting to go off the track here. True, assuming that we know nothing about either gender, than %50 of the time it would be 1 boy and 1 girl. However, this has little to do with your question. We know that one is a boy.
So, we drop the 25% of time where it is two girls, because it has nothing to do with the question (you stated that one of the children is a boy, so the probability of GG is 0%). That shrinks our sample set.

[ QUOTE ]

So fine, if you really want to say that B-G and G-B are the same, then go ahead. But as you can see by the math above, that choice is twice as likely as either of the other choices!

So fines, lets then do it like this:

BB(.25)
GG(.25)
BG(.50)


[/ QUOTE ]

Again, these numbers do not apply to your question. Given that one of children is a boy, here's the possibilities (even with the BG and GB are different idea):

If the first child is the KNOWN boy defined in the original question, then you're possibilities are:
BB(.5)
BG(.5)

If the second child is the known boy from the original question, you're possibilities are:
BB(.5)
GB(.5)

[ QUOTE ]

Going back to the original problem, we can eliminate GG because at least one of them isn't a boy. Therefore we are left with BG(.5) and BB(.25). As you can see, the 'other' kid is a girl twice as often as its a boy(.5 is 2x .25). Another way to phrase twice as likely is 66%-33%.

This really is silly as G-B and B-G are indeed separate choices, but fine do it this way.

[/ QUOTE ]
This is a misapplied understanding of probability. The flaw is that if you are going to count GB and BG as seperate instances (which actually do in both of the last two paragraphs), you need to count BB twice. You are trying to resolve two variables at one time, which is leading to the incorrect results. In other two do this, you need to first enumerate the possibilities of one variable, and then for each value of the first variable enumerate the values of the second variable (as I did done above).

You have essentially chosen a more complicated way to solve a simple problem. In the most simple form, you could just say that "order doesn't matter, BG is the same as GB, so if we know that one is a boy, the chance of the other being a boy is 50/50". However, they way you are choosing to solve it is "order DOES matter, BG is not the same as GB, and while we know that one is a boy, we don't know which one it is"; in this case the correct solution is "knowing that either one or the other is a boy, solve for the cases that first one is a boy (50/50) and then solve for the cases where the second is a boy(50/50), and then take the weighted average of the two scenerios (in this case both scenerios have an equal weight), yielding a result of ((.5 + .5)/2 = (1)/2 = .5".

[moondogg]

[ QUOTE ]
Here is why you can't 'Take him away. Lock him in a closet. Bury him in the back yard for all I care.'

I said, "one of them is male." I didn't tell you which one. So you can't just throw him away.

Bottom line: On average, a 2 kid family where one of them is male...the other one will be male 33% of the time.


[/ QUOTE ]

Response in another branch (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=886646&page=0&view=&s b=5&o=&vc=1)

[jwvdcw]

I see that I'm getting nowhere with you so:

I will pay for your airfair to meet me whenever you have time.


We will flip two coins together. Whenever one of these coin flips is a head, our bet will be on. If the other coin is also a head, then you win, if the other coin is a tail, then I win. If you say this is 50/50, then you will love this next part: I will offer you 1.5-1 odds, meaning that if you put up $100, I'll put up $150. We will do this all day long.

I am completely serious about this and willing to pay for your airfare, hotel accomodations, and even buy your food while you're out here. I only ask that we do this bet a large number of times so that short-term luck doesn't come into play.

PM me if interested. Serious inquiries only.


Please please please take me up on this. I double dog dare you!

[jwvdcw]

I'm not sure why you started another thread. I honestly don't know what else I can say to get you to understand:

Basically, theres a greater chance of a couple having one boy and one girl than them having both boys.

Its actually a 2-1 greater chance.

Thats all I'm saying and if you understand that then you'll get the question.

[Lottery Larry]

"One of them is male. What is the chance that the other one is also male?"

I see this as a 33% chance as well

Possible combinations
BB
BG
GB

Why would we consider older brother/younger sister and older sister/younger brother to be duplicates, thus eliminating one birth option to get 50%

Now if he had said "the older child is male" then it would be 50%

I don't see this as being the same as a coin flip, but is it? If I would say "I will flip a coin two times in a row. One of the times will be heads. What are the odds that the other time (NOT the next time, it could be the first time!) will be heads?" that would be 33% also- right?

Thanks
LL

[Lottery Larry]

"willing to pay for your airfare, hotel accomodations, and even buy your food while you're out here. I only ask that we do this bet a large number of times so that short-term luck doesn't come into play."

How many times would it take until you eliminate short-term luck?

[daveymck]

Your bet is not matching the original question.

Comparing your bet to the question then either coin 1 will always have to be heads or coin two will always have to be heads you then flip the other one.

[Lottery Larry]

No, he's saying flip both at once. The bet only is triggered if one of the two coins happens to be heads. If they are both tails, the bet is a push.

I thought the same thing as you at first, then reread it carefully.

[daveymck]

Yes I know what he is saying, but to match the question one of the coins has to be fixed at heads, it is only the result of the unfixed coin that we need.

His argument is based on the results of two but that results of 1 ie boy has no bearing or consideration on the result of the unknown. ie the result of the unknown child is eith B or G ages, hair colour etc are irrelevant to the question he set, the only unknown is the result of the remaining child.

To rephrase his question, I have two children aged 13 and 15, one of those is a boy, what is the probability that the other child is a boy.

By his reckoning we should be looking at

13 15

b b
g b
b g

Discounting gg as we know there is one boy. But that is flawed because we are not looking at the result of two children, we are looking at the required answer for 1 child.

13/15

B
G

Therefore its 50%.

[jwvdcw]

[ QUOTE ]
"willing to pay for your airfare, hotel accomodations, and even buy your food while you're out here. I only ask that we do this bet a large number of times so that short-term luck doesn't come into play."

How many times would it take until you eliminate short-term luck?

[/ QUOTE ]

Lets just say we'll sit around all day and play the game. I'd say we'll probably get in around 2500-5000 bets. Since the odds favor you(if you don't believe my answer), then you should love to do this.

[jwvdcw]

[ QUOTE ]
Yes I know what he is saying, but to match the question one of the coins has to be fixed at heads, it is only the result of the unfixed coin that we need.


[/ QUOTE ]

No! I'm not saying- This child is a boy. Now heres another child, what are the odds that he is a boy? That would obviously be 50%.

I'm saying. Heres two kids. When one is a boy, what are the odds that the other is a boy? The answer is 33%.

Does anyone actually know if there is info about familes' kids in the U.S.? I would love to look at all 2 kid families and see the percentages. I guarantee you that if you take all families that have at least one boy, close to 66% will have a girl as the other kid.

[moondogg]

Uhhg. You are contradicting yourself.

Here's a quick rundown of some of our conversation.

Your original question:
[ QUOTE ]

A family has two children. One of them is male. What is the chance that the other one is also male?


[/ QUOTE ]

My response (partial):
[ QUOTE ]

Here's you're sample set: 2 boys, one of each, or 2 girls.
1 boy and 1 girl is no different than 1 girl and 1 boy. %50/%50. If the order matters, you are asking a different question. What is the chance that the other is male? Well, in that case you are definitely talking about the OTHER one, not the original one you defined to be a male. This whole idea of their being two children and either one may or may not be male given that at least one or the other is male is logical slight of hand; you are completely redefining the question, and that redefinition yields a different answer. If go back the the original question you asked, the answer is %50/%50. If you want to answer to be 2/3, ask a different question.


[/ QUOTE ]

Your response:
[ QUOTE ]

But thats the thing. I didn't say, "One is male, what are the odds the other one is male." In that case, it would be 50/50.

I used the word 'IF'. That changes everything because then it is no longer telling you that one is male and asking about the other one, it is telling you that ONE OF THEM(but not telling you which one) is male. Theres a huge difference.


[/ QUOTE ]

My response:
[ QUOTE ]

[ QUOTE ]

But thats the thing. I didn't say, "One is male, what are the odds the other one is male." In that case, it would be 50/50.


[/ QUOTE ]

Actually, that IS what you said. They original question was:
[ QUOTE ]

A family has two children. One of them is male. What is the chance that the other one is also male?


[/ QUOTE ]

[ QUOTE ]

I used the word 'IF'.


[/ QUOTE ]
No you didn't.

[ QUOTE ]

That changes everything because then it is no longer telling you that one is male and asking about the other one, it is telling you that ONE OF THEM(but not telling you which one) is male. Theres a huge difference.


[/ QUOTE ]
That's why it is a different question.


[/ QUOTE ]

Your response:
[ QUOTE ]

my fault, you're right.

Here is why you can't 'Take him away. Lock him in a closet. Bury him in the back yard for all I care.'

I said, "one of them is male." I didn't tell you which one. So you can't just throw him away.

Bottom line: On average, a 2 kid family where one of them is male...the other one will be male 33% of the time.


[/ QUOTE ]

After the "my fault, you're right", I have no idea why you are continuing with this. You have already acknowledged that the answer to your question is 50/50.

According to you, if you said "One is male, what are the odds the other one is male.", then the answer would 50/50.
As demonstrated, with the exception of the world "also", that is exactly what you said (obviously, given the nature of the sentence, "also" does not change the meaning of the sentence). Hence, the answer, by your own statements, is 50/50.

It seems that whatever question you trying to ask was supposed to have an answer of 1/3, but you asked the question incorrectly. Again, according to your own statements, the answer to the specific question you asked was 50/50.

Perhaps you should try to officially restate the question, being more specific about exactly what you are asking.

[moondogg]

BTW, I am done with this thread. Now I'm going to go argue with a brick wall about what the definition of "is" is.

[jwvdcw]

1. The chance that a family's first-born child will be a boy is 50%.
2. The chance that a family's first-born child will be a girl is 50%.
3. The chance that a family's second-born child will be a boy is 50%.
4. The chance that a family's second-born child will be a girl is 50%.
5. The chance that a family's first-born child will be a boy and that its second-born child will also be a boy is obtained by multiplying the chances of each separate event -- i.e., 50% * 50% = 25%.
6. Similarly, the chance that a famly's first-born child will be a boy and that its second-born child will be a girl is 25%.
7. The chance that a family's first-born child will be a girl and its second-born child will be a girl is 25%.
8. The chance that a family's first-born child will be a girl and its second-born child will be a girl is 25%.
9. So for any two-child family, the chance that both children will be boys is 25%, he chance that both children will be girls is 25%, and the chance that they will have one girl and one boy is 50%.
10. Having one girl and one boy is thus twice as likely as having two boys.
11. Restating paragraph 10, in any two-child family, given that at least one child is a boy, it is twice as likely that the other child is a girl than it is that the other child is also a boy.
12. Restating paragrah 11, in any two-child family where at least one child is a boy (but you don't whether it's the older child, the younger child, or both), the other child has only a 33% chance of also being a boy.


Taken from Maurile Tremblay at footballguys.

[maurile]

A family has two children. One of them is male. What is the chance that the other one is also male?

I have flipped two coins. One of them landed heads. What is the chance that the other one also landed heads?

Those two games are equivalent. In each case, the answer is 1/3. The children have already been born and the coins have already been flipped, and all you know about them is that they're not girl-girl or tails-tails. Since in either case a heterogeneous result is twice as likely as any particular homogeneous result, the chance of a homogeneous result ("the other one is also male/heads") is 1/3.