The question should've stated that it assumed equal probability of a child being born as either a boy or a girl, with twins being equally likely of equal and different gender.
aaron is correct that girl-boy combination is more likely (50%), while only 25% of two-child families will have both boys, and 25% will have both girls. now that the question says that you meet a boy on the street, it now is equally likely that he will have a brother or a sister. this is because two boys in a family means that you must weight that family double (because you're twice as likely to meet a boy from that family, because there are two boys). so now the chance is 50-50 that you'll me a boy from a family with two boys or a family with a girl and a boy. but i still don't think the explanation given is correct (just because there are two choices, boy or girl, that doesn't mean that both choices have the same weighting).
Oh man, first I was arguing against the paradox, but now I have to argue for it. It actually works out...
Here's another way to think of it. What is the probability of any given gender combination in a two child family:
(25% BB) - (50% GB) - (25% GG)
We can ALL agree on that, it's simple math. All the paradox problem does is remove the GG possability. The probability of BB becomes 33%, and the probability of GB becomes 66%. Cenus data bears this out: about 50% of families are GB, making it 66% when you discard the GG families. Can't think of any other way to clarify this.
The probability that child 1 is a boy is 100% (because you've met child 1).
The probability that child 2 is a girl is 50% (equal probability boy or girl).
So the probability that, having met a boy, that his sibling is a girl is:
1*1/2 = 1/2.
That is it! That is the only answer. I asked 2 of my old stats professors, and I trust them more than peeps on this site. Plus I consulted my old stat book and prob theory book. This is the mathematical way to solve this problem.
People are getting caught up in the language, and not looking at the underlying math. Being a girl or boy is an independent event with 1/2 probability. That means, NO OTHER EVENT effects it. This is not like having 4 kids and pulling 2 out - becuase you don't have 4 kids. You only have 2 kids, each one iwth 50% probability of being a boy or girl. You don't have a set of 4 to start with, only a set of 2.
I understand what you're saying, and I'm not even going to try and explain WHY the probability works out the way it does, but if it's true that 50% of two-child families with at least one boy have one girl, then we conclude: 50% BB and 50% GB, Correct? The inverse would have to be true of families where at least one of the children is a girl: 50% GG and 50% GB. The GB in each case MUST be referring to the same families, therefore if we combine these results we have: 33% BB, 33% GB, and 33% GG in the general population. That's simply not how the world is, we know the true breakdown in the population is 25% BB, 50% GB and 25% GG. The math just seems funny because 25% of the possible outcomes are being disregarded in the paradox problem.
Oh, and your statement "So the probability that, having met a boy, that his sibling is a girl is: 1*1/2 = 1/2." is absolutely correct. Unfortunately it does not disprove the paradox, which is asking a very different question. The problem with your statement is that if you randomly meet a boy, BB families are twice as likely to be represented than GB families. Though the probability that a boy has a girl sibling IS 50%, the probability that a FAMILY with a boy also has a girl is 66.6%
So read my question again and explain how my explanation is correct but answer is wrong?
I am asking that, given 1 boy, the other child is a girl. You're talking about how many combinations of 4 children end up GB. Two different questions, no? One is about a probability in a set of 2 (my question). The other is about a percentage of results for a set of 4 (your question).
The way your question is worded, 1/2 is the correct answer. The question you are asking, however, is not the paradox question that you are trying to disprove with your explanation. The paradox question would be "if you meet a FAMILY on the street with two children, one of whom is a boy, what is the probability that the other is a girl?" The answer to that question is 2/3.
I disagree, but I don't want to argue it anymore. I have two statistics profs that agree with me, and that's good enough for me. You can have your paradox.
The question should've stated that it assumed equal probability of a child being born as either a boy or a girl, with twins being equally likely of equal and different gender.
WOW! This question can't be correct because girls are born more often then boys and that is a fact. XX versus XY .
stupid question.. easy
ahh well it can only be a boy or girl so 50/50 dont get all the other junk lol
gotta thanks genetic class ^^
math!!! no!..still i got right!@
MATH! i like it!
(giggling)
psh wut does that have to do w/ anthing?
what about a transvestite :3
good riddance!
analysis is needed..
statisctics
that's not even math~
i love math =)
wow..is it?
Math is my wrost subject! But I got it right!
wheewh.. lucky i was listening to our biology class!!^^
LOL yeay for math problems haha im a nerd lol
nigga
why do you have hard questions here so uinfair
Simple guess, even though I did work genetics problems in biology before...
aghhh
hehe...
yay, at first i was like what? but then i was like oh yeah! xD
wow loved that question xD
crazy question,but it's fun hehehe
lol
haha-- guessed it right--
wait it's actually 1/3 cuz of hermaphrodites XD
aaron is correct that girl-boy combination is more likely (50%), while only 25% of two-child families will have both boys, and 25% will have both girls. now that the question says that you meet a boy on the street, it now is equally likely that he will have a brother or a sister. this is because two boys in a family means that you must weight that family double (because you're twice as likely to meet a boy from that family, because there are two boys). so now the chance is 50-50 that you'll me a boy from a family with two boys or a family with a girl and a boy. but i still don't think the explanation given is correct (just because there are two choices, boy or girl, that doesn't mean that both choices have the same weighting).
Oh man, first I was arguing against the paradox, but now I have to argue for it. It actually works out...
Here's another way to think of it. What is the probability of any given gender combination in a two child family:
(25% BB) - (50% GB) - (25% GG)
We can ALL agree on that, it's simple math. All the paradox problem does is remove the GG possability. The probability of BB becomes 33%, and the probability of GB becomes 66%. Cenus data bears this out: about 50% of families are GB, making it 66% when you discard the GG families. Can't think of any other way to clarify this.
It doesn't work out at all!
Each is an independent event.
The probability that child 1 is a boy is 100% (because you've met child 1).
The probability that child 2 is a girl is 50% (equal probability boy or girl).
So the probability that, having met a boy, that his sibling is a girl is:
1*1/2 = 1/2.
That is it! That is the only answer. I asked 2 of my old stats professors, and I trust them more than peeps on this site. Plus I consulted my old stat book and prob theory book. This is the mathematical way to solve this problem.
People are getting caught up in the language, and not looking at the underlying math. Being a girl or boy is an independent event with 1/2 probability. That means, NO OTHER EVENT effects it. This is not like having 4 kids and pulling 2 out - becuase you don't have 4 kids. You only have 2 kids, each one iwth 50% probability of being a boy or girl. You don't have a set of 4 to start with, only a set of 2.
I understand what you're saying, and I'm not even going to try and explain WHY the probability works out the way it does, but if it's true that 50% of two-child families with at least one boy have one girl, then we conclude: 50% BB and 50% GB, Correct? The inverse would have to be true of families where at least one of the children is a girl: 50% GG and 50% GB. The GB in each case MUST be referring to the same families, therefore if we combine these results we have: 33% BB, 33% GB, and 33% GG in the general population. That's simply not how the world is, we know the true breakdown in the population is 25% BB, 50% GB and 25% GG. The math just seems funny because 25% of the possible outcomes are being disregarded in the paradox problem.
Oh, and your statement "So the probability that, having met a boy, that his sibling is a girl is: 1*1/2 = 1/2." is absolutely correct. Unfortunately it does not disprove the paradox, which is asking a very different question. The problem with your statement is that if you randomly meet a boy, BB families are twice as likely to be represented than GB families. Though the probability that a boy has a girl sibling IS 50%, the probability that a FAMILY with a boy also has a girl is 66.6%
So read my question again and explain how my explanation is correct but answer is wrong?
I am asking that, given 1 boy, the other child is a girl. You're talking about how many combinations of 4 children end up GB. Two different questions, no? One is about a probability in a set of 2 (my question). The other is about a percentage of results for a set of 4 (your question).
The way your question is worded, 1/2 is the correct answer. The question you are asking, however, is not the paradox question that you are trying to disprove with your explanation. The paradox question would be "if you meet a FAMILY on the street with two children, one of whom is a boy, what is the probability that the other is a girl?" The answer to that question is 2/3.
I disagree, but I don't want to argue it anymore. I have two statistics profs that agree with me, and that's good enough for me. You can have your paradox.