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

[Fire Daemon]

Yeah, you can deride 33% from seeing something like this but doing so from the question provided is flawed in that it essentially asks 'what is the chance that from a single birth the result is a male' which is usually 50%. I know, the second could be the boy and blah, blah, blah I've seen this before but you wouldn't tell a women with two male children that one of those children had a 66.66666% chance of being female if you knew that one of her children would be destined to be male. She would hit you or something.

EDITED

 

[SimuLord]

Think of the problem this way:
Instead of thinking "one is a boy" think "they are not both girls". Both mean the same thing.
If they are not both girls, then obviously there is a 33% chance that they are both boys.

The reason most people think that its 50% is because they interpret "one is a boy" as "the first one is a boy". That's not what it means. It means that at least one is a boy, but its still equally likely that it could be either, and half as likely that it could be both.

Not so. It said "what are the odds that the other is ALSO a boy"...in other words "what's the probability that the second child is a boy GIVEN that the first child is a boy?" The first child's gender is event A. The second child's gender is event B. Events A and B are independent.

Therefore P(B) = P (B|A) = 50%.

I reread the question, and I think you're right according to the phrasing. The way I first saw it written when I had it explained to me was "one is a boy, what are the odds that they are both boys?" In that case, the answer is 33%.

If you say 33% to that construction, you're using "one is a boy" as your sample space. The odds that they are BOTH boys if ONE is a boy is asking P (X=2|X=1), which is zero. If one is a boy, two cannot be boys. It's still not 33%.

The odds that AT LEAST one child is a boy is 75%. P(X>=1)=3/4.

There are no constructions here that would make the sample space such as to make the probability 33%.

Wait, if the given is that one is boy, wouldn't the odds that at least one is a boy be 100%?

It would. The odds of at least one boy in the entire two-child sample space is 75%. Should've made that clearer.

This has been an interesting thread insofar as it warms my heart to see that 80% of this forum has at least a basic grasp on statistics.

 

[Berethond]

The fifth panel applies to you all.

http://imgs.xkcd.com/comics/words_that_end_in_gry.png

 

[Instant K4rma]

Well, one could be a goat if you want to find a loophole.

I agree. The second child is a goat, isnt it? Damnit, I should have know.

 

[Avatar Roku]

Protip: The question basically says "what are the odds that a kid #2 is a boy, given that kid #1 is a boy, OR that kid #1 is a boy, given that kid #2 is a boy."

The people saying it's 50% are forgetting the underlined part.

Thing is, that doesn't make a difference. Either way, the given is a boy, the unknown is unknown. Either way, the given makes absolutely no difference, as (by one interpretation of this awfully worded question) the question is just asking about the unknown child's sex, not that of both children.

 

[PsiMatrix]

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

What's the answer?

50%. The other child will either be male or female, one or the other. That's the odds since there's only two possibilities.


Looking at it another way you still get 50% since in the boy-boy, boy-girl, girl-boy, girl-girl and not factoring the order of birth means we know one is a boy which eliminates the girl-girl option and boy-girl and girl-boy is the same odds-wise means we only have two options; boy-boy or boy-girl.


Factoring in the order of births we then have the girl-boy and boy-girl options as separate which is where we get 33% since the girl-girl option is still invalid.


Then we come to the last option of 25% which applies if you factor all the options in which means you have a 1 in 4 chance of it being two boys.


It would only be 100% if they were monozygotic/identical twins.


Dammit, they're all valid options.

 

[Kuchinawa212]

Well, one could be a goat if you want to find a loophole.

I agree. The second child is a goat, isnt it? Damnit, I should have know.

*laughs* I suppose now we have to assume the gender of the goat

 

[lacktheknack]

It depends. Do we include the first kid in the equation?

If so, 33%.

If not, 50%.

Easy.

 

[lacktheknack]

Think of the problem this way:
Instead of thinking "one is a boy" think "they are not both girls". Both mean the same thing.
If they are not both girls, then obviously there is a 33% chance that they are both boys.

The reason most people think that its 50% is because they interpret "one is a boy" as "the first one is a boy". That's not what it means. It means that at least one is a boy, but its still equally likely that it could be either, and half as likely that it could be both.

Oooooh, didn't think of that.

 

[Captain Wes]

Real answer is 50%

However, based on the wording of the thread it would be 0% "A women has two kids, one is a boy, what are the odds the other is also a boy?" if its a word problem its 0 if its a real question than 50%

 

[Emperor Inferno]

It has nothing to do with the gender of either child individually. The only deciding factor is whether the sperm that fertilizes the egg has a "X" chromosome or a "Y" chromosome. The chances for both are 50%.

So the answer to the question, regardless of any circumstances of other children, is 50%.

 

[SonicKoala]

It's 100%, obviously. It's too bad only 1 other person was smart enough to see that. Boys always win =D

 

[heyheysg]

It's variable probablity, but I'm not sure the question is phrased right,

The oldest kid is a boy?

anyway

Boy Boy is in
Boy Girl is in
Girl Girl is out
Girl Boy is in

So it's 33%

And the difference between "Boy Girl" and "Girl Boy" is...

Assuming this is a statistical question without empirical basis
or not a biological question

You still have to account for the fact that the children will be of different ages
Even twins aren't born at the exact same time

 

[Buffoon]

I know it's counter-intuitive, but the answer is 33%, I believe, for reasons that have been stated.

I actually found the famous '3 doors' riddle easier to comprehend (it was in that crappy film 21: 3 doors, fabulous prize behind one, crap behind the others, you pick a door, you're shown what's behind one of the other doors, then asked if you want to change your choice; intuitively you'd think it wouldn't matter, but you should always change). Made my brain hurt figuring out why, but I got there!

 

[Gmano]

Hold on, after puzzling about this for a while, i thought of an alternative...

1/2 chance of first child being girl ---> 100% chance of boy

chance of the GB 50%

1/2 chance of boy ---> 1/2 chance of girl ---> 25% chance of BG

1/2 chance of boy ---> 1/2 chance of boy ---> 25% chance of BB

25%?

 

[KittywifaMohawk]

I'm going to have to go with 50% on this one. No other answer seems logical.