Poll: A women has two kids, one is a boy, what are the odds the other is also a boy?

[Cowabungaa]

The fact that one kid is a boy has no influence on the gender of the other kid. But yeah, the question is badly worded, and therefore could have several correct answers depending on the interpretation.

 

[Rolling Thunder]

0.5, 50%, 1/2...

 

[DazZ.]

A second boy, however, does have a 1-2% higher probability of being homosexual. (I WISH I was making that up.)

Later children may not have the potential to grow as large as earlier offspring, and may also suffer intellectually.

You saying homosexuals are small idiots?

I never implied correlation between height, intelligence and homosexuality.

Twas a joke. (A hilarious one at that).

 

[fletch_talon]

Too complex to work out with the information given.

We don't know the quality of the father's Y chromosome so it could be impossible for the second child to be a boy (nothing states that there was one father for both children).

We would also need to investigate the chances of it being born a hermophrodite.

 

[orangeapples]

It all depends on the preference of the woman, and where she got the kids. If she's targeting boys then 100%. If she has no preference, then looking at the boy to girl ratio of the country (I'm using the United States since I'm in the U.S.A.) 1.05:1, then she has a 50/50 chance of finding a boy or a girl.

it also depends on the location
school: 50% boy, 50% girl
a mall: 30% boy, 70% girl
arcade: 97% boy, 3% girl

oh, you meant she gave birth to the kids...

 

[waggmd]

The options at the start can be organised like this.

B - B 25%
B - G 25%
G - B 25%
G - G 25%

At least one of them is a boy.

B - B 33%
B - G 33%
G - B 33%
G - G 0%

Thus, the probability of the other sibling being a boy is 33%

And thus this is correct.

Edit http://en.wikipedia.org/wiki/Boy_or_Girl_paradox skip down to the scientific investigation section.

* Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?"
* Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?

Two versions of the question from that wikipedia section.

Notice how both are different than the question asked.

The probability in the wikipedia article refers to a question involving BOTH kids. The question asked by the creator of this topic was directly related to ONE child.

Child a is boy.

Child b is boy (50%)
Child b is girl (50%)

The question in this case doesn't link both kids. Word the question differently and it would but until the question is reworded then the 33% is false. In this case it is worded like question one in which case as wikipedia confirms, it is in fact 50%.

Except I said skip down to the scientific investigation section which compares these two questions.

"Mr. Smith says: ?I have two children and at least one of them is a boy.' Given this information, what is the probability that the other child is a boy?"
"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?"

The OP question is similar to the first one, however both these questions are the same thing. It's just the wording is sightly different, which in turn leads to assumptions. We assume that since we know one is a boy he must be the oldest; however it is never stated in question.

so are options are:
BB
GB
BG

or 33%

This is why things like the Monty Hall problem are so interesting. They trick you into thinking something is 50/50 when its actually 66/33.

http://tierneylab.blogs.nytimes.com/2008/04/10/the-psychology-of-getting-suckered/

 

[Amnestic]

0%.

She reproduced via parthenogenesis the second time.

[sub]No, seriously, it's roughly 50%.[/sub]

so are options are:
BB
GB
BG

or 33%

Not at all. The options are:

B
G

So it's 50%. The first child is irrelevant to the calculations.

 

[Rolling Thunder]

Gah....statistics lectures....repressed memories....

 

[TZer0]

Both 33.3% and 50% are correct. It all depends on if we look at the one boy specified as unique occurrence which must be included or not.

http://en.wikipedia.org/wiki/Boy_or_Girl

 

[Booze Zombie]

50 percent seems like the obvious one at face value, but I get the feeling there's a "trick" here.

 

[Maze1125]

So it's 50%. The first child is irrelevant to the calculations.

That's the thing, it's not the first child that's a boy, it's simply one of the the children that's a boy. It could be the first child, or it could be the second. Therefore both the first and the second child are relevant.

As one guy said, don't think of it as "One is a boy." think of it as "They are not both girls." The two are equivalent, but with the second statement it is obvious that there is only a 1/3 chance of them both being boys.

 

[BaldursBananaSoap]

So where's the father of these kids? In a bar, drinking away? Shocking.

 

[Hamster at Dawn]

You already know the first one is a boy, so the probability of the second being a boy is 50%. I see what people are saying about the 33% and it makes sense but it also doesn't. If you didn't know what gender I was then you would have a 50/50 chance of guessing correctly. If I then tell you that I have a brother, that doesn't change the odds.

 

[Aesir23]

50% since the chances of getting a boy or girl in general is based on whether the egg receives either the X or the Y chromosome.

So unless the second child is a fraternal twin, then that is my answer.

You've got it backwards. The egg is always an X chromosome. The sperm is what determines, since it can be either X or Y

I know, I meant that the egg would receive either a second X chromosome resulting in a girl, or a Y chromosome resulting in a boy

 

[Takoto]

Is this a trick question, or is OP just stupid?

 

[Manicotti]

So there is a 75% chance that the other child is a girl? That really doesn't add up. It is a 50-50 chance of boy or a girl. It is regardless of how many children she has.

Please don't tell me you're that dense. Yes, it's a 50% chance for an individual child to be born as one gender or the other, but I already said that I was looking at the outcome of two children of the same gender as a single event, and calculating the chance of it accordingly.

 

[Avatar Roku]

So it's 50%. The first child is irrelevant to the calculations.

That's the thing, it's not the first child that's a boy, it's simply one of the the children that's a boy. It could be the first child, or it could be the second. Therefore both the first and the second child are relevant.

As one guy said, don't think of it as "One is a boy." think of it as "They are not both girls." The two are equivalent, but with the second statement it is obvious that there is only a 1/3 chance of them both being boys.

Not really. The known child is irrelevant, whether he's the first or second, as there's a 50% chance that the unknown is a boy, completely independent of his/her brother.

Look at it like this: a woman has two children. That means there's four options:

GG
GB
BG
BB

Obviously, given the parameters of the problem, GG is out. On the surface, it would seem that there's 3 options (BG, BB, GB) left, but, as that isn't true, since the order doesn't matter. Therefore, GB and BG are the same, meaning there's only two options, BB and BG/GB.

 

[Maze1125]

So it's 50%. The first child is irrelevant to the calculations.

That's the thing, it's not the first child that's a boy, it's simply one of the the children that's a boy. It could be the first child, or it could be the second. Therefore both the first and the second child are relevant.

As one guy said, don't think of it as "One is a boy." think of it as "They are not both girls." The two are equivalent, but with the second statement it is obvious that there is only a 1/3 chance of them both being boys.

Not really. The known child is irrelevant, whether he's the first or second, as there's a 50% chance that the unknown is a boy, completely independent of his/her brother.

Look at it like this: a woman has two children. That means there's four options:

GG
GB
BG
BB

Obviously, given the parameters of the problem, GG is out. On the surface, it would seem that there's 3 options (BG, BB, GB) left, but, as that isn't true, since the order doesn't matter. Therefore, GB and BG are the same, meaning there's only two options, BB and BG/GB.

For any given family with two children, they are twice as likely to have a boy and a girl as two boys. If you eliminate the possibility that they have two girls that does not change the fact that it they are twice as likely to have a girl and a boy as they are two boys.

 

[Maze1125]

You already know the first one is a boy, so the probability of the second being a boy is 50%. I see what people are saying about the 33% and it makes sense but it also doesn't. If you didn't know what gender I was then you would have a 50/50 chance of guessing correctly. If I then tell you that I have a brother, that doesn't change the odds.

But you don't know that the first one is boy, you only know that one of them is boy. That's a key difference.

Yes, it's true that if you had a brother it would be irrelevant to the probability of your gender, but if all we knew was that you had a sibling, and at least one of you was male, but not knowing which one, that would effect the probability of your gender.

 

[razer17]

I'm guessing 50%, but if we want to be nerds then we could factor in the rates of Fraternal Twins vs. Identical Twins, then whether the genders of Fraternal twins mostly match or not. Of course, we don't, so let's go with 50%.

Nope, its 50% X 50%, or 0.5X0.5 = 0.25%