Probability Question

sully800 · Post by **sully800** » Fri Sep 15, 2006 12:04 pm

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 · Post by **Nappy Bone Apart** » Fri Sep 15, 2006 12:41 pm

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

OwlLawyer · Post by **OwlLawyer** » Fri Sep 15, 2006 1:05 pm

Beastly · Post by **Beastly** » Fri Sep 15, 2006 2:25 pm

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

mightyal · Post by **mightyal** » Fri Sep 15, 2006 2:38 pm

This isn't a probability question. 0%

OwlLawyer · Post by **OwlLawyer** » Fri Sep 15, 2006 2:47 pm

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

Old wive's tale.

mightyal · Post by **mightyal** » Fri Sep 15, 2006 3:05 pm

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 · Post by **OwlLawyer** » Fri Sep 15, 2006 3:17 pm

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

maniacmath17 · Post by **maniacmath17** » Fri Sep 15, 2006 4:00 pm

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 · Post by **Cheesemore** » Fri Sep 15, 2006 4:03 pm

maniacmath17 wrote: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 · Post by **spiesr** » Fri Sep 15, 2006 4:04 pm

mightyal wrote: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 · Post by **sully800** » Fri Sep 15, 2006 4:49 pm

mightyal wrote: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 · Post by **Nappy Bone Apart** » Fri Sep 15, 2006 5:18 pm

sully800 wrote:
mightyal wrote: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 · Post by **spiesr** » Fri Sep 15, 2006 5:21 pm

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

spiesr · Post by **spiesr** » Fri Sep 15, 2006 5:24 pm

Nappy Bone Apart wrote:
sully800 wrote:
mightyal wrote: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 · Post by **Nappy Bone Apart** » Fri Sep 15, 2006 5:25 pm

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 · Post by **Nappy Bone Apart** » Fri Sep 15, 2006 5:26 pm

spiesr wrote: They is no such thing as BB it is 50%

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

spiesr · Post by **spiesr** » Fri Sep 15, 2006 5:28 pm

Nappy Bone Apart wrote:
spiesr wrote: 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 · Post by **Nappy Bone Apart** » Fri Sep 15, 2006 5:32 pm

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 · Post by **gavin_sidhu** » Fri Sep 15, 2006 10:13 pm

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

sully800 · Post by **sully800** » Fri Sep 15, 2006 10:46 pm

Nappy Bone Apart wrote: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 · Post by **sully800** » Fri Sep 15, 2006 10:49 pm

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 · Post by **Nappy Bone Apart** » Sat Sep 16, 2006 12:43 am

sully800 wrote: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 · Post by **vtmarik** » Sat Sep 16, 2006 10:18 am

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 · Post by **Stopper** » Sat Sep 16, 2006 1:14 pm

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....

Probability Question

What are the odds that the other child is a boy?

Probability Question