The Boy or Girl Paradox (riddle) (gtfih)

[Lopez27]

I remember my first statistic class in highschool, how cute is everyone ITT

The guy has had 2 babies. One of them is a boy. The boy is either the older one or the younger one, so thats is also another variable. It can be Older-boy/younger-girl or Older-boy/younger boy/ or older-girl/younger boy.

In this scenario you are considering the event as the 2 babies, not each baby as a separate case. Its like a coin toss; i flipped a coin twice and at least one of those times it was heads. What is the probability for the other coin flip to be heads as well? hint: its not 50%

If you cant understand this then i feel sorry for you and please never set foot on a casino ever in your life, or anywhere where you need to use your brain for that matter.

Sorry to tell you but.... yes, it is 50%. Just because you landed on one side the first time it doesn't change the coin in anyway, the coin will still have 2 sides that it could land on... giving it a 50% chance.. Simple concept.

[mynameisuntz]

"I have at least one son - what is the gender of my other child?"

You WOULD list:

1) Boy
2) Girl

You would NOT list (despite many people suggesting this):

1) Boy (BB)
2) Older girl (GB)
3) Younger girl (BG)

You also would NOT list:

1) Younger boy (BB)
2) Older boy (BB)
3) Older girl (GB)
4) Younger girl (BG)

It's 50%.

[Lailoken]

Commits gamblers fallacy.
Accuses misc of being bad gamblers.

That guy knows what he's talking about!

"Regression toward the mean simply says that, following an extreme random event, the next random event is likely to be less extreme. In no sense does the future event "compensate for" or "even out" the previous event, though this is assumed in the gambler's fallacy (and variant law of averages). Similarly, the law of large numbers states that in the long term, the average will tend towards the expected value, but makes no statement about individual trials. For example, following a run of 10 heads on a flip of a fair coin (a rare, extreme event), regression to the mean states that the next run of heads will likely be less than 10, while the law of large numbers states that in the long term, this event will likely average out, and the average fraction of heads will tend to 1/2. By contrast, the gambler's fallacy incorrectly assumes that the coin is now "due" for a run of tails, to balance out."

edit: that being said, I reread the OP and realize the wording is specifically looking to catch people so you can yell gambler's fallacy. touche.

[mynameisuntz]

i think we disagree just because you look at it as a man saying "i have one kid, he's a boy, my wife just got pregnant, what are my next kids chances of being a boy? in this case the answer is 50%.

i'm looking at it as some hobo telling me he's got two kids, 1 is a boy, what's the probability that they are BOTH boys, not that the next one WILL be a boy.

What is the difference? In the first scenario, you have a boy, and you're determining the chances of the next one being a boy. It's 50%. In the second scenario, you have a boy as is. So you can have another boy (BB) or a girl (BG/GB). It's also 50%.

Same thing.

[Ken-O]

I remember my first statistics class in college, how cute you're being.

You're still wrong. This case IS 50%.

You are mistaken my friend. Ask any statistics teacher, any REAL statistics teacher, it doesnt matter if its a bor or a girl, the answer is still 1/3.

In all seriousness, you are making a very simple mistake. You are taking each kid as a completely different scenario and it really isnt.

[anonymous]

Bunch of fail in this thread.

It's 1/3. There isn't anything to debate

/stats major

[LegosInMyEgos]

I think you both just disagree because you're both being too hard headed to realize there are 2 valid ways to interpret the question.

[mynameisuntz]

"Regression toward the mean simply says that, following an extreme random event, the next random event is likely to be less extreme. In no sense does the future event "compensate for" or "even out" the previous event, though this is assumed in the gambler's fallacy (and variant law of averages). Similarly, the law of large numbers states that in the long term, the average will tend towards the expected value, but makes no statement about individual trials. For example, following a run of 10 heads on a flip of a fair coin (a rare, extreme event), regression to the mean states that the next run of heads will likely be less than 10, while the law of large numbers states that in the long term, this event will likely average out, and the average fraction of heads will tend to 1/2. By contrast, the gambler's fallacy incorrectly assumes that the coin is now "due" for a run of tails, to balance out."

You said:

"if you are betting money on a coin toss, how many times does the coin have to land on heads before you wise up and realize it's probably going to be tails next flip? it was common sense for me long before I learned the mathematical reasoning behind it. maybe the misc doesn't gamble enough."

Which IS GAMBLERS FALLACY. Regression to the mean looks at patterns, and is more applicable to the law of large numbers. You are micro-analyzing individual trials based on previous trials, which IS gamblers fallacy.

Similar to the "hot hand fallacy." The idea of being "due."

You are mistaken my friend. Ask any statistics teacher, any REAL statistics teacher, it doesnt matter if its a bor or a girl, the answer is still 1/3.

In all seriousness, you are making a very simple mistake. You are taking each kid as a completely different scenario and it really isnt.

Explain how it is 1/3 then. Make me understand.

(BB) or (BG or GB) = 50/50. How is that wrong?

[iceypain]

"I have at least one son - what is the gender of my other child?"

You WOULD list:

1) Boy
2) Girl

You would NOT list (despite many people suggesting this):

1) Boy (BB)
2) Older girl (GB)
3) Younger girl (BG)

You also would NOT list:

1) Younger boy (BB)
2) Older boy (BB)
3) Older girl (GB)
4) Younger girl (BG)

It's 50%.

try looking at it this way. ignoring the question, do you agree that bb gg bg gb have equal probabilities? yes? then now in hindsight you know that you did not have two girls. basically the second child is not a new event, this is ex-post probability.

[anonymous]

I think you both just disagree because you're both being too hard headed to realize there are 2 valid ways to interpret the question.

no
its 1/3
there's no interpretation

[hittman]

25%

this

[Ken-O]

Sorry to tell you but.... yes, it is 50%. Just because you landed on one side the first time it doesn't change the coin in anyway, the coin will still have 2 sides that it could land on... giving it a 50% chance.. Simple concept.

No, im aware that the universe doesnt keep a record of the numbers of heads that have landed on a coin flip. Thats the gamblers fallacy, a very common mistake for newcomers to las vegas lol.

In this case, tho, the 2 coin flips are part of the same experiment. We dont know whether the first flip was heads or was it the second, and that does matters believe it or not. Think about it, lets say you going to flip a coin twice. Your possible results are as follow:

Heads/Tails
Tails/Heads
Heads/Heads
Tails/Tails

If we know that at least one of the coin flip landed on heads, then we know the tails/tails result is impossible. That leave us with 3 possible results.


Very easy to grasp once you understand it TBH.

[mynameisuntz]

try looking at it this way. ignoring the question, do you agree that bb gg bg gb have equal probabilities? yes? then now in hindsight you know that you did not have two girls. basically the second child is not a new event, this is ex-post probability.

But the order does not matter. BG = GB. They are one in the same, leaving BB as the second option. Hence:

(BB) or (BG or GB).

No, im aware that the universe doesnt keep a record of the numbers of heads that have landed on a coin flip. Thats the gamblers fallacy, a very common mistake for newcomers to las vegas lol.

In this case, tho, the 2 coin flips are part of the same experiment. We dont know whether the first flip was heads or was it the second, and that does matters believe it or not. Think about it, lets say you going to flip a coin twice. Your possible results are as follow:

Heads/Tails
Tails/Heads
Heads/Heads
Tails/Tails

If we know that at least one of the coin flip landed on heads, then we know the tails/tails result is impossible. That leave us with 3 possible results.


Very easy to grasp once you understand it TBH.

Still 50/50

One flip was heads? So that leaves us with:

T/H
H/T
H/H

T/H = H/T as order does not matter which you just stated.

(HH) or (HT or TH) = 50/50

Now if you said, "before I flip this coin, what is the chance of hitting heads twice" - THEN it changes. 1/3 if order doesn't matter, 1/4 if order matters.

[hiimzac]

What is the difference? In the first scenario, you have a boy, and you're determining the chances of the next one being a boy. It's 50%. In the second scenario, you have a boy as is. So you can have another boy (BB) or a girl (BG/GB). It's also 50%.

Same thing.

the difference is one is a discrete probability and the other is a best guess based on a probability distribution.

[iceypain]

But the order does not matter. BG = GB. They are one in the same, leaving BB as the second option. Hence:

(BB) or (BG or GB).

order does not matter but hetero gender pairs are twice as likely as having a 2 boy pair. "or" means you're adding the probability of both.

[Ken-O]

But the order does not matter. BG = GB. They are one in the same, leaving BB as the second option. Hence:

(BB) or (BG or GB).

You are pretty much saying that the chances for the guy to have two boys is 50%, so are the chances for the guy to have a boy first then a girl (50%) or having a girl first then a boy (another 50%)

Thats 150% son.

Again, having a boy first then a girl is a complete different scenario than having a girl first then a boy, in this specific question

[mynameisuntz]

the difference is one is a discrete probability and the other is a best guess based on a probability distribution.

It's still 50/50.

order does not matter but hetero gender pairs are twice as likely as having a 2 boy pair.

That's only true if order matters, which it does not, because then each hetero possibility is its own entity. If order doesn't matter, then GB = BG, and that is what we're dealing with here.

[Lopez27]

No, im aware that the universe doesnt keep a record of the numbers of heads that have landed on a coin flip. Thats the gamblers fallacy, a very common mistake for newcomers to las vegas lol.

In this case, tho, the 2 coin flips are part of the same experiment. We dont know whether the first flip was heads or was it the second, and that does matters believe it or not. Think about it, lets say you going to flip a coin twice. Your possible results are as follow:

Heads/Tails
Tails/Heads
Heads/Heads
Tails/Tails

If we know that at least one of the coin flip landed on heads, then we know the tails/tails result is impossible. That leave us with 3 possible results.


Very easy to grasp once you understand it TBH.

No, it does not matter because the flips are independent of each other.

[hiimzac]

so if someone told you he had two kids, 1 is a boy, you'd say there was a 50% chance that both his kids were boys?

[mynameisuntz]

You are pretty much saying that the chances for the guy to have two boys is 50%, so are the chances for the guy to have a boy first then a girl (50%) or having a girl first then a boy (another 50%)

Thats 150% son.

Again, having a boy first then a girl is a complete different scenario than having a girl first then a boy, in this specific question

The chances for a guy to have two boys when we already know one is a boy is 50/50.

And no, order does not matter in this question. How do you figure there's a difference between having a boy first or a girl first? Where does that play into this?

so if someone told you he had two kids, 1 is a boy, you'd say there was a 50% chance that both his kids were boys?

Yes.

BB
BG
GB

Those are the possibilities when one is a boy, but seeing as to how order has no role, GB and BG are equivalent and are not separate entities. Hence me saying: (BB) or (BG or GB).

[waitwho]

Do not care really. 5:1 girl ratio. just seemingly pleasanter. Get duh C0ck rock hard bro.

[Lopez27]

so if someone told you he had two kids, 1 is a boy, you'd say there was a 50% chance that both his kids were boys?

No, you would figure the other would be a girl. But this is a hypothetical question, not real life buddy.

[iceypain]

It's still 50/50.



That's only true if order matters, which it does not, because then each hetero possibility is its own entity. If order doesn't matter, then GB = BG, and that is what we're dealing with here.

look, gb=bg does not preclude the fact that [gb=bg] happens twice as often as [bb]

[Ken-O]

But the order does not matter. BG = GB. They are one in the same, leaving BB as the second option. Hence:

(BB) or (BG or GB).



Still 50/50

One flip was heads? So that leaves us with:

T/H
H/T
H/H

T/H = H/T as order does not matter which you just stated.

(HH) or (HT or TH) = 50/50

Now if you said, "before I flip this coin, what is the chance of hitting heads twice" - THEN it changes. 1/3 if order doesn't matter, 1/4 if order matters.

This right here is where you are wrong.

T/H its not the same as H/T. Two completely different results each one with its own probability of happening.

[AboveAverage]

All you "stats" ****s must have made a killing with all your probability bullsh!t when the Lions went 0-16.

(not srs)

The part I'm having trouble is this scenario:

What if a casino came up with a new table games. Two coin flips, the first flip is just a practice flip. Now, on the second coin toss, would my odds be 50% or 67%?

[hiimzac]

awwww ****, untz is right. the chance of the other kid being a boy is indeed 50%, i read the question wrong, wellthisisawkward.jpg

apologies for the condescension earlier, was a little heated from the guy on the first page talking intellectual smack

[Lailoken]

You said:

"if you are betting money on a coin toss, how many times does the coin have to land on heads before you wise up and realize it's probably going to be tails next flip? it was common sense for me long before I learned the mathematical reasoning behind it. maybe the misc doesn't gamble enough."

Which IS GAMBLERS FALLACY. Regression to the mean looks at patterns, and is more applicable to the law of large numbers. You are micro-analyzing individual trials based on previous trials, which IS gamblers fallacy.

Similar to the "hot hand fallacy." The idea of being "due."

you realize "micro-analyzing individual trials based on previous trials" while a reasonable description of what occurs in gambler's fallacy, is also a reasonable description of what occurs when you look at the pattern occuring and make assumptions based on known variables and previous data...

edited: derp i cant read, need to sleep

[Lopez27]

So here is what the 33% people believe and this is how they are wrong...

They are also seeing it as a 2 variable equation, when the OP clearly stated they were independent.

[Ken-O]

The chances for a guy to have two boys when we already know one is a boy is 50/50.

And no, order does not matter in this question. How do you figure there's a difference between having a boy first or a girl first? Where does that play into this?
.

But we dont now which one is the boy. That is the key of our problem.

It is really a very simple question and this one is usually the problem that professors open their statistic classes with. I've taken about 3 different statistic classes over HS and college and in every single one of them we have studied this problem. Any teacher should be familiar with it, if you still dont understand it take it to a professor and have him explain to you how it works and maybe he will explain it better.

[demoniclizard]

Isn't it 0%, as in the other one has to be a girl.

If we follow the assumption that the ratio of girls to boys must be 50:50.

That means for every boy there must be a girl.

/thread