Probability question

[yersinia29]

I have 2 children, one is a boy. what is the prob that the other is also a boy?

A) 1/2
B) 1/3
C) 1/4
D) Not enough information to determine
E) Poorly worded question that involves subjective determination

 

[Bronze Dog]

I'd say A) 1/2, assuming that it's 50/50 for each child's gender. The second child's gender is independent of the first's.

 

[bmillsap]

A famous conditional probability question. 1/3.

 

[Moose]

1/4, because you didn't nail down which specific child (eldest or youngest) is the boy.

Of the four possibilities (B-B, B-G, G-B, G-G), there's only one possibility where both children are boys.

 

[bmillsap]

1/4, because you didn't nail down which specific child (eldest or youngest) is the boy.

Of the four possibilities (B-B, B-G, G-B, G-G), there's only one possibility where both children are boys.

...but one of those, G-G, is eliminated by the condition 'one is a boy.' So, of the remaining three (presumably equally likely) possibilities, in one of them, the other child is also a boy.

 

[Moose]

Good point.

 

[Jorghnassen]

1/3, though it's really a little bit more than that (the probability of giving birth to a boy is actually slightly bigger than .5 IIRC).

 

[Bronze Dog]

I have 2 children, one is a boy. what is the prob that the other is also a boy?

A) 1/2
B) 1/3
C) 1/4
D) Not enough information to determine
E) Poorly worded question that involves subjective determination

Am I reading something horrifically wrong, here?

Two children (4 possibilities at this point)
One is a boy (G-G eliminated, 3 possibilities)
What is the probability of the other being a boy? (2 possibilities: B-G and B-B, since we're talking about the undetermined child, rather than having any chance of picking the known boy.)

 

[Beth]

Re: Re: Probability question

Am I reading something horrifically wrong, here?

Two children (4 possibilities at this point)
One is a boy (G-G eliminated, 3 possibilities)
What is the probability of the other being a boy? (2 possibilities: B-G and B-B, since we're talking about the undetermined child, rather than having any chance of picking the known boy.)

You read it the same way I do. I'll go with 1/2 too.

Beth

 

[Orangutan]

The second child exists in a quantum state until it is observerd.
Have you or anyone else looked at the child? If so the probability that it is a boy is either 1 or 0 depending on your observation.
If it has not been observed it is 1 and 0. If it is zero it is not neserserally a girl.

It could be a cat.

O.

 

[bmillsap]

The key here, though, is you don't know who's supposed to be the 'other' child. You don't know that the FIRST child is a boy, just that one of them is. If you assume that boys and girls are equally likely, there are four possible birth orders for two children:

Boy then boy
Boy then girl
Girl then boy
Girl then girl

Of these four, one is known not to be the case since we're told one child is a boy. This leaves:

B-B
B-G
G-B

But, as noted above, each of these are equally likely. So, of these possible ways to have at least one boy, in how many cases are both children boys? One. Out of? Three.

Remember, the key here is that no one defined a 'primary' and 'other' child. If the question were 'my first child was a boy, what's the chance the other one is too?' then the answer would be 1/2. But you don't know that piece of information.

 

[CurtC]

1/3

 

[Orangutan]

Ok seriously,

The sex of the other child is not important. I might as well tell you I own a car.

Re-worded the question.

I have a child you don't know the sex of.
What is the chance that it is a boy?

So I plump for 1/2 too. (assuming equal probablility of boy/girl).

O.

 

[Bronze Dog]

The key here, though, is you don't know who's supposed to be the 'other' child. You don't know that the FIRST child is a boy, just that one of them is. If you assume that boys and girls are equally likely, there are four possible birth orders for two children:

Boy then boy
Boy then girl
Girl then boy
Girl then girl

Of these four, one is known not to be the case since we're told one child is a boy. This leaves:

B-B
B-G
G-B

But, as noted above, each of these are equally likely. So, of these possible ways to have at least one boy, in how many cases are both children boys? One. Out of? Three.

Remember, the key here is that no one defined a 'primary' and 'other' child. If the question were 'my first child was a boy, what's the chance the other one is too?' then the answer would be 1/2. But you don't know that piece of information.

The confusion I'm having that doesn't seem to be addressed is that one line specifies that one child is a boy, followed immediately by a question about the other child, which I infer to be the one other than the known boy.

If it was phrased, "I have two children. One of them is a boy. What are the chances my second-born child is a boy?", then it would be 1/3.

 

[patnray]

Beware of hidden assumptions: Are they your offspring or adopted?

 

[patnray]

Are they identical twins?

 

[gnome]

The confusion I'm having that doesn't seem to be addressed is that one line specifies that one child is a boy, followed immediately by a question about the other child, which I infer to be the one other than the known boy.

If it was phrased, "I have two children. One of them is a boy. What are the chances my second-born child is a boy?", then it would be 1/3.

Actually if you specify the second-born child the probability becomes 1/2.

A good way of wording it would be... "I have two children. At least one of them is a boy. What is the probability that both are boys?"

If you want to throw out the red herring of birth order... label them instead child A and child B without regard to order:

You have three possibilities:
Child A Boy, Child B Boy
Child A Girl, Child B Boy
Child A Boy, Child B Girl

Leaving you with the answer of 1/3.

 

[back2basics]

The second child exists in a quantum state until it is observerd.
Have you or anyone else looked at the child? If so the probability that it is a boy is either 1 or 0 depending on your observation.
If it has not been observed it is 1 and 0. If it is zero it is not neserserally a girl.

It could be a cat.

O.

No, no, no.. a boy exists in one universe, while the girl exists in another universe Depending on the wavelength of the string, depends on which universe you are observing and therefore which child you see born.

So the chance of a boy is 100% and the chance if a girl is also 100%.

 

[drkitten]

The confusion I'm having that doesn't seem to be addressed is that one line specifies that one child is a boy, followed immediately by a question about the other child, which I infer to be the one other than the known boy.

If it was phrased, "I have two children. One of them is a boy. What are the chances my second-born child is a boy?", then it would be 1/3.

This is exactly backwards. You are correct in considering this to be a conditional probability problem, but your reasoning is very precisely wrong.

The phrase "second-born child" specifics a person uniquely and the sex distribution is the same as the overall sex distribution (approximately 50-50, more accurately about 105-100 in favor of a boy for the United States).

The phrase "other child" does not uniquely specify a child; if both children are boys, then the "other child" could be either one. So you need to apply case analysis, which gives about chance in three that the other child is in fact a boy.

 

[Number Six]

Considering the way the question is worded, which is "I have 2 children, one is a boy. what is the prob that the other is also a boy?" I think the answer is both "not enough information" and "poorly worded question."