Probability Question

[sully800]

I've been in the midst of a heated debate with others regarding this probability question. I'd like to hear your unbiased opinion before I explain. (This is not a trick either... just logic). I figured its appropriate for this site sicne we all rely on logic and probability...

Carefully read:

A woman has 2 children. One of them is a boy. What is the probability the other is a boy?

[Nappy Bone Apart]

I voted 50/50, but there's not enough information. It comes down to the genetic makeup of the father's sperm.

[OwlLawyer]

50%

[Beastly]

an old wise tale says if the woman had a orgasm during conception.. it is a boy.

[mightyal]

This isn't a probability question. 0%

[OwlLawyer]

an old wise tale says if the woman had a orgasm during conception.. it is a boy.

Old wive's tale.

[mightyal]

Perhaps the desired answer is 33%. With 2 children you can have GG, GB, BG or BB. It can't be GG and of the other 3 only 1 has 2 boys.

But I'm sticking with 0%. The question says clearly that she has one boy. Therefore the other is a girl.

[OwlLawyer]

Without knowing whether or not they are from the same father, you cannot answer anything but 50%.

[maniacmath17]

The question is pretty much just asking what are the chances that a child born to this woman is a boy, which would have to be 50%. As far as I know, the other child being a boy has no impact on the sex of the boy in question.

[Cheesemore]

The question is pretty much just asking what are the chances that a child born to this woman is a boy, which would have to be 50%. As far as I know, the other child being a boy has no impact on the sex of the boy in question.

agreed, this is a stupid question

[spiesr]

Perhaps the desired answer is 33%. With 2 children you can have GG, GB, BG or BB. It can't be GG and of the other 3 only 1 has 2 boys.

But I'm sticking with 0%. The question says clearly that she has one boy. Therefore the other is a girl.

That doesn't make sense.

Note: All women are XX and men XY So it's 50%

[sully800]

Perhaps the desired answer is 33%. With 2 children you can have GG, GB, BG or BB. It can't be GG and of the other 3 only 1 has 2 boys.

But I'm sticking with 0%. The question says clearly that she has one boy. Therefore the other is a girl.

Mightyal is on top of things!

It's not a trick question, so the "one is a boy" was not meant to throw you off. That statement doesn't mean "one and only one"

However going by probability he is on the right track. Everyone says 50% and the events are independent. I thought so too at first when I saw this question.

But keep in mind it doesn't say "the youngest child is a boy, what is the chance she has another boy"

it says "one child is a boy, what is the chance the other child is a boy".

Does that change the minds of any of you 50/50 people?

[Nappy Bone Apart]

Perhaps the desired answer is 33%. With 2 children you can have GG, GB, BG or BB. It can't be GG and of the other 3 only 1 has 2 boys.

But I'm sticking with 0%. The question says clearly that she has one boy. Therefore the other is a girl.

Mightyal is on top of things!

It's not a trick question, so the "one is a boy" was not meant to throw you off. That statement doesn't mean "one and only one"

However going by probability he is on the right track. Everyone says 50% and the events are independent. I thought so too at first when I saw this question.

But keep in mind it doesn't say "the youngest child is a boy, what is the chance she has another boy"

it says "one child is a boy, what is the chance the other child is a boy".

Does that change the minds of any of you 50/50 people?

Uhm... hell no. It's a logical fallacy to say 33%.

[spiesr]

Saying one is a boy is not the same as saying only one is a boy.

[spiesr]

Perhaps the desired answer is 33%. With 2 children you can have GG, GB, BG or BB. It can't be GG and of the other 3 only 1 has 2 boys.

But I'm sticking with 0%. The question says clearly that she has one boy. Therefore the other is a girl.

Mightyal is on top of things!

It's not a trick question, so the "one is a boy" was not meant to throw you off. That statement doesn't mean "one and only one"

However going by probability he is on the right track. Everyone says 50% and the events are independent. I thought so too at first when I saw this question.

But keep in mind it doesn't say "the youngest child is a boy, what is the chance she has another boy"

it says "one child is a boy, what is the chance the other child is a boy".

Does that change the minds of any of you 50/50 people?

Uhm... hell no. It's a logical fallacy to say 33%.

They is no such thing as BB it is 50% You can be XY (boy) or XX (girl) that is it!

[Nappy Bone Apart]

I see where you're going with this, tho. You're saying that on a probability scale, 2 children give 25% GG, 50% BG or GB, and 25% BB. You remove the GG option, and you have 66.7% BG or GB, and 33.3% BB. There is your logical fallacy.

[Nappy Bone Apart]

They is no such thing as BB it is 50%

Huh? See my next post, I think we're in agreement.

[spiesr]

They is no such thing as BB it is 50%

Huh? See my next post, I think we're in agreement.

I don't get you. You said 33% and gave 4 options there are 2 & 50%.

[Nappy Bone Apart]

Sorry, I went a little quick. If you didn't know the sex of either child, then the probability of having 2 girls is 25%. 2 boys, 25%. 1 of each, 50%. Our original poster, I think, is trying to say since you know 1 of them is a boy, that changes the table by removing the chance of having 2 girls. Thus, the probability of having 1 of each is now 66.7%, and of having 2 boys 33.3%. Is is a logical fallacy, because it's still trying to look at the 2 children as 1 unique event, when since he has stipulated 1 of them must be a boy, he has separated the two, and now you're left with the 50/50 chance you'll get a girl or boy. It's a logic puzzle.

[gavin_sidhu]

Its 50% I had a biology test on Wednesday with approximately the same question.

[sully800]

Sorry, I went a little quick. If you didn't know the sex of either child, then the probability of having 2 girls is 25%. 2 boys, 25%. 1 of each, 50%. Our original poster, I think, is trying to say since you know 1 of them is a boy, that changes the table by removing the chance of having 2 girls. Thus, the probability of having 1 of each is now 66.7%, and of having 2 boys 33.3%. Is is a logical fallacy, because it's still trying to look at the 2 children as 1 unique event, when since he has stipulated 1 of them must be a boy, he has separated the two, and now you're left with the 50/50 chance you'll get a girl or boy. It's a logic puzzle.

You have the exact same thinking as me now but are arriving at a different answer and I'm not sure what you think the logical fallacy is.

As you said, the only 4 options are GG, BG, BB, and GB. Since we know one is a B that leaves 3 choices. BB is only one of those 3. What's wrong with that logic?

If the question was "the first child is a boy...what are the odds the second child is a boy?" then I agree it would be 50%.

But as you said, there are 3 options and the answer we are looking for is 1 of those 3. Hence the 33%

[sully800]

Think of it this way....if you surveyed every family of 2 children in the world, with at least one boy. You really think 50% of them would have 2 boys?

There are 2 ways to arrive at 1 boy and 1 girl. So the frequency will occur twice as much...and only 1/3 of the families will have 2 boys.

I know how you feel though because I was thinking the same thing for a while.

(I'm going to have to bump my plane puzzle soon....that got almost no views here at first but has started VERY heated arguments every where else I've seen it.)

[Nappy Bone Apart]

Think of it this way....if you surveyed every family of 2 children in the world, with at least one boy. You really think 50% of them would have 2 boys?

There are 2 ways to arrive at 1 boy and 1 girl. So the frequency will occur twice as much...and only 1/3 of the families will have 2 boys.

I know how you feel though because I was thinking the same thing for a while.

(I'm going to have to bump my plane puzzle soon....that got almost no views here at first but has started VERY heated arguments every where else I've seen it.)

This is a totally different situation. The only way your logic would work in your original question is if both children were born at the same time. Then you would have a 33% probability the second twin was a boy. But since you've stipulated one child is already there, and now you're seeking the probability of the sex of the second child, it becomes a seperate probability equation. You can't combine the 2 unless they're twins.

In this other question, you're discovering the sex of both at once, thus you can combin the probabilities into one box again, and arrive at your 3 combinations of sexes when you remove 1 girl possibility.

The interesting thing is totally correct logic leads you to both answers. You an also use correct logic to arrive at a completely different answer of yours. Since you know with 100% certainty one of them is a boy, and the chance of the other being a boy is 50/50, then logically, you would have an average chance of 75% of having BB. Totally wrong, yet logical.

[vtmarik]

Well, since the male carries the determining X or Y, the odds are 50/50. There's no question about this "GB, BB, BG" thing, it's incidental and has no real bearing on the probability of the matter. The female can only produce one gene, the X (since gametes are half of our chromosomes, and females have XX) but guys can produce both X and Y, it's all about how the genes get split.

The real probability question is the likelihood of twins and the gender of those twins.

[Stopper]

I don't know if anyone has mentioned this yet, but there's a helpful page on Wikipedia for this:

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

It seems that the wording of the question is all-important - the way it's been worded on this thread though, I'd say it was 50/50 here.

EDIT: I'm almost tempted to start a thread on the Monty Hall problem....