Probability Question

[OwlLawyer]

I think the question should read: Given that a woman has two children and atleast one is a boy, what are the chances that both are boys?

There we go. This I can get behind.[/quote]

Um, that's still 50%.

[Nappy Bone Apart]

I think the question should read: Given that a woman has two children and atleast one is a boy, what are the chances that both are boys?

There we go. This I can get behind.

Um, that's still 50%.[/quote]

Is it? I didn't really think about it much. You're right. The question should read: A woman has twins. One of them is a boy. What is the probability the other is a boy?

As I argued earlier, that makes the conception of both one event, and your probability box will work here. Otherwise, it's still 2 seperate events.

[OwlLawyer]

Is it? I didn't really think about it much. You're right. The question should read: A woman has twins. One of them is a boy. What is the probability the other is a boy?

As I argued earlier, that makes the conception of both one event, and your probability box will work here. Otherwise, it's still 2 seperate events.

Well, there you would have to know about twin birth probabilities too. It's a different question.

[vtmarik]

I'm not. Using wikipedia as your only source to prove a theory leaves much to be desired. That "core" can't check every page once a year, much less a week or whatever. wikipedia is a great resource, but I wouldn't accept it as law.

The pages are checked daily, every edit is reviewed by the community and if there is a problem the edit is redacted and the original page restored.

[OwlLawyer]

So it's democratically elected fact

[vtmarik]

So it's democratically elected fact

No, it's referenced fact added in by members of the community.

[sully800]

I think the question should read: Given that a woman has two children and atleast one is a boy, what are the chances that both are boys?

I agree.

[sully800]

Same fallacy we've been discussing all thread.

EXPLAIN THE FALLACY

You have said multiple times that its faulty logic but have never provided any evidence as to WHY its faulty logic. Disprove Maniac's coin flip example, because thats the exact same problem I'm talking about.

[Stopper]

A lot's happened here since I last posted - I also agree with what maniacmath said - my only bone of contention was with the way the original question was worded, which seemed to me to reduce the question to the single event of the second child, which would leave 50/50...

As for Wikipedia, it was I who left the link here - I didn't leave it to prove my theory or anything like that, and I dare say Wikipedia isn't 100% accurate, far from it, but if you read the article yourself (and don't rely on any rapidly-editing "core"), it seems to explain in a concise manner where possible confusions might arise from.

[Nappy Bone Apart]

Same fallacy we've been discussing all thread.

EXPLAIN THE FALLACY

You have said multiple times that its faulty logic but have never provided any evidence as to WHY its faulty logic. Disprove Maniac's coin flip example, because thats the exact same problem I'm talking about.

sully. Stop taking this personally. I've explained it 5 different times. Go back, read. You're right, the coin flip example is the same problem. Exactly the same. And you're looking at it in exactly the wrong way. You're wanting to look at 2 seperate, unique coinflips as 1 probability question. THAT CANNOT BE DONE. OwlLawyer has also explained the fallacy. In your question, you're trying to combine the probability of the sex of 2 seperate, unique children. If they were twins, you could oversimplify this question to fit your theory. But since you offer no reference of time, actually I believe the correct answer to this question would be "Not enough information". As I've posted earlier, you can twist logic to fit any answer from 0% to 100% to your question. Fix the question, and then someone can give a definitive answer.

[guest84]

I think I agree with Sully here. At first I thought it was 50%, and that it was independent, but now I think that's only the correct answer if the question was "A woman has a boy. What is the probability that her next child will be a boy?" In this case it's an independent event and the probability would be 50%. However, if we know that she has two children, and 1 boy, then the possibilities would be BB, BG, GB, GG. Removing the GG would leave 1 of 3 where there are 2 boys, or 33.3%.

[sully800]

sully. Stop taking this personally. I've explained it 5 different times. Go back, read. You're right, the coin flip example is the same problem. Exactly the same. And you're looking at it in exactly the wrong way. You're wanting to look at 2 seperate, unique coinflips as 1 probability question. THAT CANNOT BE DONE. OwlLawyer has also explained the fallacy. In your question, you're trying to combine the probability of the sex of 2 seperate, unique children. If they were twins, you could oversimplify this question to fit your theory. But since you offer no reference of time, actually I believe the correct answer to this question would be "Not enough information". As I've posted earlier, you can twist logic to fit any answer from 0% to 100% to your question. Fix the question, and then someone can give a definitive answer.

I'm not taking it personally, I just don't understand where you are coming from. What maniac and I have written does not seem to be what you are describing, so it seems like you have never listened to our logic.

You flip a coin once and its heads. What is the probability that the next flip is heads? 50%. I get that, so I am not making the mistake that you and OwlLawyer described so many times. I think everyone understands that.

You flip a coin twice which of course yields two results. At least one is heads. What is the probability that both flips were heads? 33%. That's what maniac and I are saying, and its a different situation than the one you are describing. You absolutely can view the data as one instance in this case because the two flips do not happen sequentially (at least not that you can tell from the given data). For all intents and purposes they happen concurrently and time is irrelevent. I don't know how else to describe it other than the 4 possibilities again. HH, TT, TH and HT in this game. You know TT is not a choice so its 1 in 3. There is nothing wrong with that logic, at least that you have proven.

[sully800]

And sorry, I missed this part of your 4th post I guess

"It 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"

Every previous time you mentioned it you simply said "that's a logical fallacy" and that's what irked me because you offered no explanation.

The whole point of the puzzle though, once again, is that there is no reference to time. That doesn't make the problem unsolvable or incomplete- It means that you have to treat the data as one event essentially because you don't know what happened first. I don't know how else to explain it, and why you don't agree because you seemed to understand where I was coming from in your 3rd and 4th posts. However I sincerely believe the chance is not 50% and that if you look at maniac's wording of the coin flip problem (to eliminate any of the confusion people had with mine) it proves that 33% is the correct answer.

[zarvinny]

I believe that this whole 33% balderdash is all wrong.

Lets stop looking at this in BB GG BG terms and look at it a more normal way.
The question says the family has one boy and one x (boy or girl)

First, if the boy was first born, then the second born child will be a girl (50%) or a boy (50%).

If the boy was second born, then his older sibling is either a girl (50%) or a boy (50%).

Therefore, the answer is 50%.

If you look at all the 2 child families on earth with at least 1 boy, 1/2 of them will have a girl, and 1/2 of them will not.

Unless I misunderstood the question, here it is, plain as dirt.

[Nappy Bone Apart]

The whole point of the puzzle though, once again, is that there is no reference to time. That doesn't make the problem unsolvable or incomplete- It means that you have to treat the data as one event essentially because you don't know what happened first. I don't know how else to explain it, and why you don't agree because you seemed to understand where I was coming from in your 3rd and 4th posts. However I sincerely believe the chance is not 50% and that if you look at maniac's wording of the coin flip problem (to eliminate any of the confusion people had with mine) it proves that 33% is the correct answer.

Ah. I believe there is our divergence. In the absense of a timeframe, I CAN'T assume it's one event. I can't assume ANYTHING and still fit within a logical framework. When you make an assumption, it becomes a theory, not logical fact. If you do assume it as one event, then you're correct. If you don't, then I'm most likely correct. Therefore, I guess it comes down to what assumptions you make about the question itself.

Interesting discussion, tho.

[mightyal]

I believe that this whole 33% balderdash is all wrong.

Lets stop looking at this in BB GG BG terms and look at it a more normal way.
The question says the family has one boy and one x (boy or girl)

First, if the boy was first born, then the second born child will be a girl (50%) or a boy (50%).

If the boy was second born, then his older sibling is either a girl (50%) or a boy (50%).

Therefore, the answer is 50%.

If you look at all the 2 child families on earth with at least 1 boy, 1/2 of them will have a girl, and 1/2 of them will not.

Unless I misunderstood the question, here it is, plain as dirt.

you count one instance twice. When there are 2 boys, you count it as both boy 1st and boy 2nd.
You can test this with a coin. Toss it twice, ignore hh (GG)and record how often you get tt (BB).If you are being serious with this twins idea, toss two coins simultaneously. I am confident that will give the same result after enough tries.

[Kernal_Kronic]

It's 50%...It's either a boy or a girl, so there's it's 1 in 2 chance

[sully800]

If you look at all the 2 child families on earth with at least 1 boy, 1/2 of them will have a girl, and 1/2 of them will not.

Unless I misunderstood the question, here it is, plain as dirt.

I think you're wrong on that. I do believe you would have twice as many mixed sex children as families with 2 boys.

Take the coin data because people seem to find it less confusing.

You flip 100 coins....assuming perfect numbers this would give you 50 heads and 50 tails. Now you flip each of those coins again. Of the 50 original heads, 25 would land heads and 25 would land tails. Of the 50 original tails, 25 would land heads and 25 would land tails. This yeilds 25 of each result: HH, TT, TH and HT.

Just like the boy and girl situations, the mixed set appears twice as frequently as the other two. So if I told you one of the flips was heads, the chance of it being a head/tail combo is 66% and only 33% for a double heads flip.

Of course this only applies for the rule of large numbers, so the data won't come out that way exactly in 100 rolls. This is a simplified version but it doesn't matter if you roll 100 times or 1,000,000- the answer will be the same.

THERE it is, plain as dirt.

[sully800]

I believe that this whole 33% balderdash is all wrong.

Lets stop looking at this in BB GG BG terms and look at it a more normal way.
The question says the family has one boy and one x (boy or girl)

First, if the boy was first born, then the second born child will be a girl (50%) or a boy (50%).

If the boy was second born, then his older sibling is either a girl (50%) or a boy (50%).

Therefore, the answer is 50%.

If you look at all the 2 child families on earth with at least 1 boy, 1/2 of them will have a girl, and 1/2 of them will not.

Unless I misunderstood the question, here it is, plain as dirt.

you count one instance twice. When there are 2 boys, you count it as both boy 1st and boy 2nd.
You can test this with a coin. Toss it twice, ignore hh (GG)and record how often you get tt (BB).If you are being serious with this twins idea, toss two coins simultaneously. I am confident that will give the same result after enough tries.

mightyal has it right again.

You can't take two 50% chances, give a 50% chance of each happening...and then say the answer is 50%. That would be 25%.

You are giving 25% chance that its BG, 25% that its BB....and 25% that its GB and 25% that its BB. The only reason this is adding up to 50 is because you counted the BB situation twice, one for each of the two scenarios.

[Nappy Bone Apart]

Sully, let's go have a beer. This is getting silly.

One last question. What real world application does any of this have, other than to give us somethig to stretch our minds over?

[Nappy Bone Apart]

You can't take two 50% chances, give a 50% chance of each happening...and then say the answer is 50%. That would be 25%.

lol I can't help myself. You're not taking two 50% chances. You're taking one 100% chance and one 50%. By stipulating one has to be a boy, you take one 50% chance out of the equation, leaving the other. Thus, 50%.

Simple as dirt.

[colinb007]

its a simple matter of boy girl, 50 / 50.
because it also could be any father who would have genes for boy/girl
still 5o/5o
its totaly random boy or girl
50/50

and someone probaly said the same thing because i havent read the complete forum.

[sully800]

You can't take two 50% chances, give a 50% chance of each happening...and then say the answer is 50%. That would be 25%.

lol I can't help myself. You're not taking two 50% chances. You're taking one 100% chance and one 50%. By stipulating one has to be a boy, you take one 50% chance out of the equation, leaving the other. Thus, 50%.

Simple as dirt.

This really is silly indeed.

But I'm still right and youre not

[Nappy Bone Apart]

nuh uh!