Poll of the Day > Help me understand your reasoning in solving the following easy problem

(+) Yeah! (+)

It seems like a somewhat nonsensical question that in real life would have more details that make the answer more obvious, basically a waste of thought.

It's 50% if you look at from one point of view and 33% from another. That's nonsense.

jamieyello3 posted...

It seems like a somewhat nonsensical question that in real life would have more details that make the answer more obvious, basically a waste of thought.

It's 50% if you look at from one point of view and 33% from another. That's nonsense.

That's like saying probability is nonsense because in real life you can just look at your lotto numbers and tell if you won or not.

Umm, unless I'm missing something it is definitely 50%.
The one explanation I saw for 33% is that you have 4 possibilities

BB
BG
GB
GG

So assuming BB is impossible, you would conclude 33%. That is flawed logic. The reason for that is that you assume BG and GB are different events and GG and BB are not. What you should have written is:
BB
BG or GB (same thing)
GG

You eliminate BB and you are left with 50% probability of GG.

Another way to do this:
BB
BB
BG
GB
GG
GG

Eliminate the BB and you are still left with 50%. If you're going to state BG and GB are different, then you have to say GG happens x2 as well.

Drews1315 posted...

Another way to do this:
BB
BB
BG
GB
GG
GG

Eliminate the BB and you are still left with 50%. If you're going to state BG and GB are different, then you have to say GG happens x2 as well.

What if you didn't eliminate the BB? What if it were just a totally random family? You're telling me that there's a 33% chance of them having two girls?
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Ann, Courtney
Heidi, Bradley
Gary, Emily
Derek, Fred

If you were to randomly choose one of those 4 girls, you'd have a 2 in 4 chance, 50%, of having a family of two sisters, right?

If you had 1000 people, 500 girls and 500 boys, and 125 girl-girl pairs, 125 boy-boy pairs, and 250 girl-boy pairs, you'd still have a 50% chance, if you randomly picked a girl, that the girl would have a sister and not a brother, right?

I understand that GB and BG are different, and combined, are twice as common as GG. I just don't understand how it's not offset by GG being twice as likely to be picked as GB, and twice as likely to be picked as BG, since there are two random girls to pick from instead of just one, which offsets GG being less common. One of the explanations in that link seemed to agree with my line of thinking here, though that link seemed to argue what the proper way to interpret the problem was, too.
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Drews1315 posted...

Umm, unless I'm missing something it is definitely 50%.
The one explanation I saw for 33% is that you have 4 possibilities

BB
BG
GB
GG

So assuming BB is impossible, you would conclude 33%. That is flawed logic. The reason for that is that you assume BG and GB are different events and GG and BB are not. What you should have written is:
BB
BG or GB (same thing)
GG

You eliminate BB and you are left with 50% probability of GG.

Another way to do this:
BB
BB
BG
GB
GG
GG

Eliminate the BB and you are still left with 50%. If you're going to state BG and GB are different, then you have to say GG happens x2 as well.

If you have two children, having a boy first and a girl second is obviously different than having a girl first and a boy second. That's why you have BG and GB, but not BB and BB. The second BB would be like saying the younger child is the older brother.

If you flip two coins you have:

HH - 25%
HT - 25%
TH - 25%
TT - 25%

Hopefully we can all agree on that at least? So why would you combine BG and GB in TC's question but not for flipping two coins?

Another way to look at it. You have a room full of people that flip two coins. You tell everyone that flipped at least one heads to stay, and those who flipped two tails must leave. Now pick a person from the room at random and what is the chance they flipped two heads? I'm hoping that everyone will agree it's 33%, but I'm curious how many think that's wrong, and how many think that's a different question than TC's.
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Drews1315 posted...

So assuming BB is impossible, you would conclude 33%. That is flawed logic. The reason for that is that you assume BG and GB are different events and GG and BB are not. What you should have written is:
BB
BG or GB (same thing)
GG

BG and GB *are* different events, though. Having a boy, then a girl is not the same event as having a girl, then a boy. The order does actually matter, even though it doesn't seem like it should.

Consider it this way: suppose I introduce you to "Alice". Alice is a mother of two. I tell you that one of her two children is a girl.

Alice HAD to have given birth to the two children in a set order. Even if they were twins delivered by C-section, one of 'em popped out first. She either gave birth to a girl, followed by another girl, a girl followed by a boy, or a boy followed by a girl (the fourth possibility - a boy followed by another boy - is impossible given that you know for certain one of the children is a girl). Ergo, the odds of of her having two girls is 33% (note that WHICH girl came out first doesn't matter, because it produces a statistically identical result).

Now, I can change up the situation by telling you that Alice's eldest child is a girl. In that case, the odds are 50%, because one of the remaining options - boy followed by girl - is now eliminated.

Again, the slight statistical trickery here is that you're not being told the order of birth, which is actually important. Many people get tripped up on that because, intuitively, when you hear "one of the children is a girl", you think of "the other child" as "the next child", which is not the same thing.
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Golden Road posted...

Ann, Courtney
Heidi, Bradley
Gary, Emily
Derek, Fred

If you were to randomly choose one of those 4 girls, you'd have a 2 in 4 chance, 50%, of having a family of two sisters, right?

If you had 1000 people, 500 girls and 500 boys, and 125 girl-girl pairs, 125 boy-boy pairs, and 250 girl-boy pairs, you'd still have a 50% chance, if you randomly picked a girl, that the girl would have a sister and not a brother, right?

I understand that GB and BG are different, and combined, are twice as common as GG. I just don't understand how it's not offset by GG being twice as likely to be picked as GB, and twice as likely to be picked as BG, since there are two random girls to pick from instead of just one, which offsets GG being less common. One of the explanations in that link seemed to agree with my line of thinking here, though that link seemed to argue what the proper way to interpret the problem was, too.

The problem here is that you're assigning identifiers to the girls in the form of names. If you do that, you're obscuring the problem by making each child unique.

An easier way to conceptualize it is to make this a different binary choice, one that isn't easily anthropomorphized - like coin tosses. And, for another way of making this easier to visualize, we'll change the number of tosses from two to four.

So here's my modified version of the problem. Let's say I tell you I'm going to flip four coins. I do so in private, then reveal three of the coins: all three are heads. What are the odds the fourth coin is also heads?

The answer is not 50% - it's less.

Intuitively this makes sense - we know instinctively that if we randomly toss a bunch of coins in the air it's more likely to have a "mix" of heads and tails rather than all of one or the other. The more spelled out answer is that there's only one way for the hidden coin to be heads (if I tossed four heads), but four ways for the hidden coin to be tails (if the first flip was tails, or the second, or the third, or the fourth). Thus, the actual answer is 20%.

It's the same with the problem given. Imagine I tell you a family has six kids and five of them are boys - do you, intuitively, think it's more likely that the sixth is also a boy or that the parents - through sheer force of probability if nothing else - managed at least one pair of X chromosomes in their babymaking efforts?
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A woman I do not know walks up to me at the park, because she wants to jump my bones, a girl in tow. We small talk, during which she tells me she has another kid playing on the slide. I ask her 'boy or girl?'. Would I expect the chances of each to be 50/50?

darkknight109 posted...

Golden Road posted...

Ann, Courtney
Heidi, Bradley
Gary, Emily
Derek, Fred

If you were to randomly choose one of those 4 girls, you'd have a 2 in 4 chance, 50%, of having a family of two sisters, right?

If you had 1000 people, 500 girls and 500 boys, and 125 girl-girl pairs, 125 boy-boy pairs, and 250 girl-boy pairs, you'd still have a 50% chance, if you randomly picked a girl, that the girl would have a sister and not a brother, right?

I understand that GB and BG are different, and combined, are twice as common as GG. I just don't understand how it's not offset by GG being twice as likely to be picked as GB, and twice as likely to be picked as BG, since there are two random girls to pick from instead of just one, which offsets GG being less common. One of the explanations in that link seemed to agree with my line of thinking here, though that link seemed to argue what the proper way to interpret the problem was, too.

The problem here is that you're assigning identifiers to the girls in the form of names. If you do that, you're obscuring the problem by making each child unique.

An easier way to conceptualize it is to make this a different binary choice, one that isn't easily anthropomorphized - like coin tosses. And, for another way of making this easier to visualize, we'll change the number of tosses from two to four.

So here's my modified version of the problem. Let's say I tell you I'm going to flip four coins. I do so in private, then reveal three of the coins: all three are heads. What are the odds the fourth coin is also heads?

The answer is not 50% - it's less.

Intuitively this makes sense - we know instinctively that if we randomly toss a bunch of coins in the air it's more likely to have a "mix" of heads and tails rather than all of one or the other. The more spelled out answer is that there's only one way for the hidden coin to be heads (if I tossed four heads), but four ways for the hidden coin to be tails (if the first flip was tails, or the second, or the third, or the fourth). Thus, the actual answer is 20%.

It's the same with the problem given. Imagine I tell you a family has six kids and five of them are boys - do you, intuitively, think it's more likely that the sixth is also a boy or that the parents - through sheer force of probability if nothing else - managed at least one pair of X chromosomes in their babymaking efforts?

Dude, you are great at explaining this.

It's basically a spin on this

https://en.m.wikipedia.org/wiki/Monty_Hall_problem
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darkknight109 posted...

Golden Road posted...

Ann, Courtney
Heidi, Bradley
Gary, Emily
Derek, Fred

If you were to randomly choose one of those 4 girls, you'd have a 2 in 4 chance, 50%, of having a family of two sisters, right?

If you had 1000 people, 500 girls and 500 boys, and 125 girl-girl pairs, 125 boy-boy pairs, and 250 girl-boy pairs, you'd still have a 50% chance, if you randomly picked a girl, that the girl would have a sister and not a brother, right?

I understand that GB and BG are different, and combined, are twice as common as GG. I just don't understand how it's not offset by GG being twice as likely to be picked as GB, and twice as likely to be picked as BG, since there are two random girls to pick from instead of just one, which offsets GG being less common. One of the explanations in that link seemed to agree with my line of thinking here, though that link seemed to argue what the proper way to interpret the problem was, too.

So here's my modified version of the problem. Let's say I tell you I'm going to flip four coins. I do so in private, then reveal three of the coins: all three are heads. What are the odds the fourth coin is also heads?

The answer is not 50% - it's less.

Intuitively this makes sense - we know instinctively that if we randomly toss a bunch of coins in the air it's more likely to have a "mix" of heads and tails rather than all of one or the other. The more spelled out answer is that there's only one way for the hidden coin to be heads (if I tossed four heads), but four ways for the hidden coin to be tails (if the first flip was tails, or the second, or the third, or the fourth). Thus, the actual answer is 20%.

Expanding on this a bit, let's say that after revealing that three are heads, you say that the first coin you flipped was heads. Now there are only three ways for the hidden coin to be tails, improving the odds of it being heads to 1/4 or 25%. If you also said that the third coin you flipped was heads, then the odds of the hidden coin being heads is 33%. And finally, if you also said that the fourth coin you flipped was heads, then we know the hidden coin was the second coin, and the odds of that being heads is 50%. For some reason people are thinking they know which of the four coins is the hidden one.
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stha guy posted...

That's like saying probability is nonsense because in real life you can just look at your lotto numbers and tell if you won or not.

Yes, but you can either assume you started with two kids chosen at random, and then calculate the odds, or you can assume you start with one predefined child, which is a 50/50. The way you get the answer 33% is by making a lot of assumptions about how you got this data. You end up with some broken logic with no real world application, and a lot of confusion for the sake of confusion, because people confuse complexity with just a poorly designed question.

The coin question and the sibling question are similar, really. Really, the main difference is that one uses coins, and one uses people, but that's a pretty important difference.

Coins are coins. They aren't very distinct, and aren't generally worth much. Technically, you could get a room full of people to flip two pennies. Without watching, you could have everyone who flipped two heads to mark the back of their pennies with a marker. Then you could have everyone who flipped at least one head place their head-landed pennies head-side up on a table. If you chose a penny at random from that table, there would be about a 50% chance the back will be marked, and it will be a penny from a double header flip. Little ridiculous to do it that way, but point is, it's possible to manipulate the setup to get that 50%. More sensibly, it's going to be 33%. Any non-convoluted setup will make it 33%.

People are not coins, though, and it doesn't make a lot of sense to treat people as interchangeably as coins. Sure, you could, but aside from a math thought problem, why? If you meet a girl who has one sibling, there's about a 50% chance her sibling is a girl, not 33%.

So ultimately, on one hand, as a thought experiment sort of thing, 33% could be correct. In real life though, it's almost always going to be 50% instead.
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i would say rationally it's a 50% chance, just by looking at the question and how i was taught in school.

But them my brain is going to overdrive. Do you think a woman is a girl? Do you consider one of the parents is a girl? is this a same sex "marriage"? Is this family a single parent? Are there even parents involved in this at all (is the family just consit of the siblings). How big is this family that we are talking about uncle and aunts, cousin and grandparents (like a family reunion)? I knew some aunts that were 6 year old and they all lived together.
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Golden Road posted...

People are not coins, though, and it doesn't make a lot of sense to treat people as interchangeably as coins. Sure, you could, but aside from a math thought problem, why? If you meet a girl who has one sibling, there's about a 50% chance her sibling is a girl, not 33%.

Not true. Here's why.

Let's pretend, for sake of our experiment here, there are 800 million people in the world who have exactly one sibling (younger or older); the rest are single children or have more than one sibling. If the distribution was perfectly random, we would expect to see that 800m consisting of 400m boys and 400m girls. Subdividing further, it should look like the following:
a) 200m girls with a sister
b) 200m girls with a brother (from category c)
c) 200m boys with a sister (from category b)
d) 200m boys with a brother

Now, this initially seems to support your hypothesis that if you meet a girl, there's a 50% chance she has a sister and a 50% chance she has a brother. After all, if you meet a girl, she has to fit in one of the first two categories, which gives you even odds that her sibling is of either gender.

The problem is, using this approach, you're actually double-counting the people in groups a and d. This is because you're not actually picking "just a girl", you're picking a pairing of siblings - when you make your initial "pick" (always guaranteed to be a girl), a second pick is automatically generated (the sibling). Groups b and c consists of 200m pairings (200m girls with 200m boys), but Group a consists of only 100m pairings (100m girls with the other 100m girls in that same group). In essence, grouping the siblings as above would only be valid if you could have Girl A be Girl B's sister, but at the same time have Girl B not be Girl A's sister, which is clearly impossible. This becomes easier if we group them by older siblings. We would expect, based on the above distribution:

a) 100m Sister-sister pairings
b) 100m Brother-sister pairings
c) 100m Sister-brother pairings
d) 100m Brother-brother pairings

Thus, you are still more likely to pick a sister with a brother than vice versa, simply because there are twice as many permutations and combinations that would yield a sister-and-brother pair than a double-sister pair. Basically - and this is a little hard to get your head around at first - because the sisters in Group A are all sisters of each other, it "concentrates" them together, whereas the girls in Groups B and C are more "spread out".

Again, this is much easier to conceptualize if you increase the number of siblings. We instinctively know that if a family has 10 kids, it's far more likely that those kids are a mix of boys and girls rather than all of one gender. The same is true on a smaller scale with two siblings, just not as pronounced (and far more vulnerable to outlier skew).
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yutterh posted...

But that is already cut down because we know one is a girl. GB is the exact same as BG, you guys are adding to much complications on to this. Who ever is the first born does not matter. Why are you guys bringing that into this?

because we're talking about the chances of having given birth to children with respect to gender. GB and BG are differently gendered outcomes... even if you consider them to be the same thing, you'd still have to give it 50% of the odds vs GG and BB, because GB/BG (considered as the same thing) is twice as likely to have occurred as GG.

GG 1/4
BB 1/4
BG/GB 2/4

remove BB, which is what the question really says, and what are we left with?

GG 1/3
BG/GB 2/3
chance of GG = 33%

whether or not you consider them the same thing, flipping Heads/Tails or Tails/Heads is twice as likely to occur as flipping Heads/Heads.

yet another way to say it is:
there is equal chance of the siblings being different as there is of them being the same. what is the chance of them being the same if we rule out one of the ways in which they can be the same? (BB).
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darkknight109 posted...

Golden Road posted...

People are not coins, though, and it doesn't make a lot of sense to treat people as interchangeably as coins. Sure, you could, but aside from a math thought problem, why? If you meet a girl who has one sibling, there's about a 50% chance her sibling is a girl, not 33%.

Not true. Here's why.

Let's pretend, for sake of our experiment here, there are 800 million people in the world who have exactly one sibling (younger or older); the rest are single children or have more than one sibling. If the distribution was perfectly random, we would expect to see that 800m consisting of 400m boys and 400m girls. Subdividing further, it should look like the following:
a) 200m girls with a sister
b) 200m girls with a brother (from category c)
c) 200m boys with a sister (from category b)
d) 200m boys with a brother

Now, this initially seems to support your hypothesis that if you meet a girl, there's a 50% chance she has a sister and a 50% chance she has a brother. After all, if you meet a girl, she has to fit in one of the first two categories, which gives you even odds that her sibling is of either gender.

The problem is, using this approach, you're actually double-counting the people in groups a and d. This is because you're not actually picking "just a girl", you're picking a pairing of siblings - when you make your initial "pick" (always guaranteed to be a girl), a second pick is automatically generated (the sibling). Groups b and c consists of 200m pairings (200m girls with 200m boys), but Group a consists of only 100m pairings (100m girls with the other 100m girls in that same group). In essence, grouping the siblings as above would only be valid if you could have Girl A be Girl B's sister, but at the same time have Girl B not be Girl A's sister, which is clearly impossible. This becomes easier if we group them by older siblings. We would expect, based on the above distribution:

a) 100m Sister-sister pairings
b) 100m Brother-sister pairings
c) 100m Sister-brother pairings
d) 100m Brother-brother pairings

Thus, you are still more likely to pick a sister with a brother than vice versa, simply because there are twice as many permutations and combinations that would yield a sister-and-brother pair than a double-sister pair. Basically - and this is a little hard to get your head around at first - because the sisters in Group A are all sisters of each other, it "concentrates" them together, whereas the girls in Groups B and C are more "spread out".

Again, this is much easier to conceptualize if you increase the number of siblings. We instinctively know that if a family has 10 kids, it's far more likely that those kids are a mix of boys and girls rather than all of one gender. The same is true on a smaller scale with two siblings, just not as pronounced (and far more vulnerable to outlier skew).

You can make long posts trying to explain something like this but it doesn't change the fact that if there's 2 people and one is 100% guaranteed to be female then that means there's only a 50% chance that her sibling is make or female since there are only two people involved.
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Revelation34 posted...

You can make long posts trying to explain something like this but it doesn't change the fact that if there's 2 people and one is 100% guaranteed to be female then that means there's only a 50% chance that her sibling is make or female since there are only two people involved.

Eh? Dude, the answer is factually 33%. We're just trying to help people understand why, since it's a little counterintuitive at first blush.
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Lightning Bolt posted...

Revelation34 posted...

You can make long posts trying to explain something like this but it doesn't change the fact that if there's 2 people and one is 100% guaranteed to be female then that means there's only a 50% chance that her sibling is make or female since there are only two people involved.

Eh? Dude, the answer is factually 33%. We're just trying to help people understand why, since it's a little counterintuitive at first blush.

No the answer is 50% for a fact. If there are only two people and you know the gender of one of those people then the other person's gender is only a 50% chance. For it to be 33% there would need to be 3 people. That is how math works.
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Revelation34 posted...

You can make long posts trying to explain something like this but it doesn't change the fact that if there's 2 people and one is 100% guaranteed to be female then that means there's only a 50% chance that her sibling is make or female since there are only two people involved.

This is only true if you specify which one is guaranteed to be female. If you say "I have two people here - the first one is a girl", then yes, the second has a 50% chance of being either male or female. But if you say "I have two people here and at least one of them is female", then there's only a 33% chance that both are female.

It's counter-intuitive, but trust me, it's true.
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Revelation34 posted...

and you know the gender of one of those people

you don't know the gender of a definite person, you know the gender of an indefinite person; it could be either the older or younger of the two who's gender you know.
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Revelation34 posted...

No the answer is 50% for a fact. If there are only two people and you know the gender of one of those people then the other person's gender is only a 50% chance. For it to be 33% there would need to be 3 people. That is how math works.

You're making a very fundamental error in how you're approaching this problem. Specifically, you're thinking in terms of a sequence. You're thinking "If I see a girl, what's the odds that the next person I see will be a girl" - in that situation, your answer - 50% - would be correct.

But that's not the question being asked. You're not being asked about the "next" person, you're being asked about the "other" person, which is not the same thing. You're being given incomplete information about a pairing, not a sequence. 50% is the intuitive answer here, but it's also the wrong one.
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Revelation34 posted...

Lightning Bolt posted...

Revelation34 posted...

You can make long posts trying to explain something like this but it doesn't change the fact that if there's 2 people and one is 100% guaranteed to be female then that means there's only a 50% chance that her sibling is make or female since there are only two people involved.

Eh? Dude, the answer is factually 33%. We're just trying to help people understand why, since it's a little counterintuitive at first blush.

No the answer is 50% for a fact. If there are only two people and you know the gender of one of those people then the other person's gender is only a 50% chance. For it to be 33% there would need to be 3 people. That is how math works.

Eh, I ended up googling it. It's just a famous question you know, with a posted answer. The answer was intended to be 33%, but the writer of it later admitted that, depending on assumptions, it could be ambiguous. I really don't see the ambiguity but whatever.

https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
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Lightning Bolt posted...

Revelation34 posted...

Lightning Bolt posted...

Revelation34 posted...

You can make long posts trying to explain something like this but it doesn't change the fact that if there's 2 people and one is 100% guaranteed to be female then that means there's only a 50% chance that her sibling is make or female since there are only two people involved.

Eh? Dude, the answer is factually 33%. We're just trying to help people understand why, since it's a little counterintuitive at first blush.

No the answer is 50% for a fact. If there are only two people and you know the gender of one of those people then the other person's gender is only a 50% chance. For it to be 33% there would need to be 3 people. That is how math works.

Eh, I ended up googling it. It's just a famous question you know, with a posted answer. The answer was intended to be 33%, but the writer of it later admitted that, depending on assumptions, it could be ambiguous. I really don't see the ambiguity but whatever.

https://en.wikipedia.org/wiki/Boy_or_Girl_paradox

You don't understand the ambiguity? The question is very barebones and fails to elaborate on whether it wants the probability of the combination GG or if it just wants the independent probability of the other child being a girl. You can easily interpret it either way.
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chaosbowser posted...

The question is very barebones and fails to elaborate on whether it wants the probability of the combination GG or if it just wants the independent probability of the other child being a girl.

It says "at least one child is a girl". That means the combination.
If it were asking about the chances independently, the question would firstly be too obvious to bother with, and secondly be phrased really awkwardly.
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25%

"At least one of them is a girl" is a red herring. The prior knowledge in no way modifies the total chances. That is to say, every family with two children has a 25% chance to have both girls.
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Sahuagin posted...

you don't know the gender of a definite person, you know the gender of an indefinite person; it could be either the older or younger of the two who's gender you know.

Which doesn't matter. There are still only two people.
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Revelation34 posted...

Sahuagin posted...

you don't know the gender of a definite person, you know the gender of an indefinite person; it could be either the older or younger of the two who's gender you know.

Which doesn't matter. There are still only two people.

Probabilities work a certain way...

the way I see it, when you think about the question being posed, you imagine in your head you've "chosen" the "first" girl even if they haven't been assigned an order. you need to unimagine the first girl and look at the bigger picture. so it's 33%.
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The trick to the question is actually pretty simple.

Both answers are correct. Which one is correct simply depends on the question you are asking/how you interpret the question that is asked.

In the event you have a single family which you have already identified a specific one of the children is a girl, that leaves one unidentified child, which thus has a 50% chance of being male/female. Or if you want to get technical, you have a 50% chance of guessing if you guess truly at random, because their gender already exists, you just don't know what it is yet (the child is not a Shrodinger's Cat, its gender doesn't resolve upon us looking at it).

In the event you are either asking or interpreting it to mean ALL families and thus have not actually identified one of the children yet, then you are looking at all families with two children that have at least one girl. In that case, you go with
BB
BG
GB
GG

You ignore BB of course because it doesn't have at least 1 girl. Leaving three configurations.
Which means that, of ALL families that have at least 1 girl among 2 children, 33~% of them have 2 girls, and the other 66~% have a boy. Which is just the 25/50/25% distribution after you remove BB.

In short. If you have already identified one of the children, its 50%. If you have not identified any children yet, then for convenience we assume someone else has removed all the 2-boy families from your sample of families. Which leaves you with a 33% chance of getting one with 2 girls in it from among all families in the sample.
.
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Revelation34 posted...

Which doesn't matter. There are still only two people.

and you don't know anything in particular about either of them
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Lightning Bolt posted...

the writer of it later admitted that, depending on assumptions, it could be ambiguous. I really don't see the ambiguity but whatever.

it says "depending on how you found out that one child was a boy". (gender is swapped in the wiki version). which again means it's only 50% if you know the gender of a definite child. (if you saw one of them or something.)
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I do not know why but i finally understand the GB BG thing hahahaha just woke up and im like "oh okay i get it now" hahhaha but i still feel it is a silly probability thing lol
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iwantmyoldid posted...

Revelation34 posted...

Sahuagin posted...

you don't know the gender of a definite person, you know the gender of an indefinite person; it could be either the older or younger of the two who's gender you know.

Which doesn't matter. There are still only two people.

Probabilities work a certain way...

Exactly. The probability of out of two = 50%.

Sahuagin posted...

and you don't know anything in particular about either of them

You know the gender of one and that's all that matters.
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Revelation34 posted...

Exactly. The probability of out of two = 50%.

You either win the lotto or you dont. Two choices. Are you now going to tell me it is 50 50?

Revelation34 posted...

You know the gender of one and that's all that matters.

You don't know which one, though. That also matters.
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iwantmyoldid posted...

Revelation34 posted...

Exactly. The probability of out of two = 50%.

You either win the lotto or you dont. Two choices. Are you now going to tell me it is 50 50?

If only two people are playing a lottery and there is a guaranteed winner, yes.

dancer62 posted...

50%. Knowing the results of one coin toss does not affect the probability of another coin toss.

I thought this was the best answer. Easy to understand and straight to the point.

RedPixel posted...

dancer62 posted...

50%. Knowing the results of one coin toss does not affect the probability of another coin toss.

I thought this was the best answer. Easy to understand and straight to the point.

Sure, but you're not just talking about one "coin toss", you're talking about a series of them. If I flip 10 coins and tell you at least nine of them came up heads, that does not mean the remaining one has 50/50 odds of being heads, because it could be tails if ANY ONE of the 10 flips turned up tails, whereas it could only be heads if ALL the 10 flips turned up heads.

I mean, think of it from the perspective of dice if you find it easier. What's the most common result on a roll of two six-sided dice? Seven, right?

But... why? After all, the result of one die roll is not affected by the result of the other. The odds of rolling a 3 and a 4 (in that order) are no different than the odds of rolling two 6s. The difference is that there's more permutations and combinations of dice rolls that provide a result of 7 (1-and-6, 2-and-5, etc.) than the dice rolls that yield a result of 12 (6-and-6 only).

Same with our problem here. There's more combinations that result in a brother (boy, then girl/ girl, then boy) than that result in a sister (girl, then girl).
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This is why scientists can't agree. Misuse of properties.

Hence why the answer is that BOTH are correct. It depends on how you ask/interpret the question.

If you have already identified a specific one of the children, the odds of the other unidentified one are 50/50 since you are only identifying one 50/50 chance.

If you have not identified one, and are just pulling randomly from a suitably large sample of families that all have at least 1 girl, the odds are 33/66.
.
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DarknessLink7 posted...

A family has two children, and at least one of them is a girl. What is the probability that they have two girls?

darkknight109 posted...

RedPixel posted...

dancer62 posted...

50%. Knowing the results of one coin toss does not affect the probability of another coin toss.

I thought this was the best answer. Easy to understand and straight to the point.

Sure, but you're not just talking about one "coin toss", you're talking about a series of them.

I see where you're coming from, but that isn't what the question asks.

The question asks what the probability is of the next child being a girl if one is already a girl. It's the same probability as a coin toss: 50%. The previous child/coin has already been decided and doesn't affect the next probability.

It'd be different if the question was reworded, which is what I believe you're thinking of-- probability and sequences. If that was the case, then the answer would not be 50%.

RedPixel posted...

The question asks what the probability is of the next child being a girl if one is already a girl.

This is where you're incorrect - no, the question doesn't ask about the "next" child. If it did, your answer - 50% - would be right. But you haven't identified which of the children is the girl and that is an important detail. It's not asking about the "next" child, it's asking about the "other" child - those aren't the same thing. Hence the answer is 33%.
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darkknight109 posted...

RedPixel posted...

The question asks what the probability is of the next child being a girl if one is already a girl.

This is where you're incorrect - no, the question doesn't ask about the "next" child. If it did, your answer - 50% - would be right. But you haven't identified which of the children is the girl and that is an important detail. It's not asking about the "next" child, it's asking about the "other" child - those aren't the same thing. Hence the answer is 33%.

Yes it is. This isn't even semantics. Both of those literally mean the same shit.
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Revelation34 posted...

darkknight109 posted...

RedPixel posted...

The question asks what the probability is of the next child being a girl if one is already a girl.

This is where you're incorrect - no, the question doesn't ask about the "next" child. If it did, your answer - 50% - would be right. But you haven't identified which of the children is the girl and that is an important detail. It's not asking about the "next" child, it's asking about the "other" child - those aren't the same thing. Hence the answer is 33%.

Yes it is. This isn't even semantics. Both of those literally mean the same shit.

"Next" means you know something about A and are being asked about B. "Other" means you know something about A or B (and it's not specified which) and are being asked about the one you don't have information about.

The question - as stated - indicates that you know A or B is a girl; not that you know A is a girl. That makes a difference in terms of the statistics involved.

If it were "next", you would know A is a girl and B is unknown, with a 50% chance of being a girl or a boy.

But it's not. Instead, based on the information given, either A is a girl and B is a boy, A is a boy and B is a girl, or both A and B are girls. Hence the answer of 33%.
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darkknight109 posted...

"Next" means you know something about A and are being asked about B. "Other" means you know something about A or B (and it's not specified which) and are being asked about the one you don't have information about.

The question - as stated - indicates that you know A or B is a girl; not that you know A is a girl. That makes a difference in terms of the statistics involved.

If it were "next", you would know A is a girl and B is unknown, with a 50% chance of being a girl or a boy.

But it's not. Instead, based on the information given, either A is a girl and B is a boy, A is a boy and B is a girl, or both A and B are girls. Hence the answer of 33%.

I appreciate you specifying why there's a different between "next" and "other", but I'm curious why there is a difference.

I'm on the 33% side, but I just can't figure out how to refute the following:

"Since we know one of the kids is a girl, there are only two scenarios: Either the first kid is the girl, and then there's a 50% chance the second kid is a girl, or the second kid is the girl, and then there's also a 50% chance the first kid is a girl. Since both scenarios give us a 50% chance both are girls, and one of the scenarios must be true, 50% is the answer."

Could you help me dissect this argument and find out where it goes wrong? I lie awake at night trying to figure this out. XD
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2 Children, 4 possibilities.
BB
BG
GB
GG

If order matters and at least one is a girl that eliminates anything starting with B.
GB
GG

1 out of 2 is GG.
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SKARDAVNELNATE posted...

2 Children, 4 possibilities.
BB
BG
GB
GG

If order matters and at least one is a girl that eliminates anything starting with B.
GB
GG

1 out of 2 is GG.

Okay, now you 50%ers are just trying to get under my skin.
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darkknight109 posted...

Revelation34 posted...

darkknight109 posted...

RedPixel posted...

The question asks what the probability is of the next child being a girl if one is already a girl.

This is where you're incorrect - no, the question doesn't ask about the "next" child. If it did, your answer - 50% - would be right. But you haven't identified which of the children is the girl and that is an important detail. It's not asking about the "next" child, it's asking about the "other" child - those aren't the same thing. Hence the answer is 33%.

Yes it is. This isn't even semantics. Both of those literally mean the same shit.

"Next" means you know something about A and are being asked about B. "Other" means you know something about A or B (and it's not specified which) and are being asked about the one you don't have information about.

The question - as stated - indicates that you know A or B is a girl; not that you know A is a girl. That makes a difference in terms of the statistics involved.

If it were "next", you would know A is a girl and B is unknown, with a 50% chance of being a girl or a boy.

But it's not. Instead, based on the information given, either A is a girl and B is a boy, A is a boy and B is a girl, or both A and B are girls. Hence the answer of 33%.

Again it doesn't matter. You know the gender of one of them 100%. It doesn't matter which one it is because there are only two people involved. In order for it to be 33% there has to be 3 people involved.
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