OK, I used to think it was 50% (and I admitted I could be wrong). But now that zit and fhmesq have explained it I believe it is 2/3. Here's the original:
"A man tells you he has two children. He then starts talking about his son. He does not tell you whether the son is the oldest child or the youngest child. What is the probability that his other child is a girl?"
What are the possibilities?
Older child = son, younger child = son: doesn't fit
Older child = daughter, younger child = son: fits
Older child = son, younger child = daughter: fits
We cannot allow both children being daughters because this is not a possibility.
How many of the possibilities I mention fit the man having a daughter? 2
How many of the possibilities I mention don't fit the man having a daughter? 1
So we have 2 possibilities out of 3 that fit or 67%.
The daughter could be the older child or the younger child and therefore should be taken separately, not together.
"A man tells you he has two children. He then starts talking about his son. He does not tell you whether the son is the oldest child or the youngest child. What is the probability that his other child is a girl?"
What are the possibilities?
Older child = son, younger child = son: doesn't fit
Older child = daughter, younger child = son: fits
Older child = son, younger child = daughter: fits
We cannot allow both children being daughters because this is not a possibility.
How many of the possibilities I mention fit the man having a daughter? 2
How many of the possibilities I mention don't fit the man having a daughter? 1
So we have 2 possibilities out of 3 that fit or 67%.
The daughter could be the older child or the younger child and therefore should be taken separately, not together.
The thinking that leads to the wrong answer is to focus on one
individual in your brain, and then switching over to the other child.
Instead, think about the fact that all you know is that this family
has two kids, and all you know is that at least one of them is male.
Given that information, the chance that they have a girl is 2/3.
Because, it's twice as likely that they have one of each
(BG or GB), that it is that they had two boys.
Zit is right here.
I didn't see it till I broke it down in to coin tosses.
We know a coin was tossed twice. We know that heads came up at least once but we don't know on which toss. What are the odds that tails came up on the other toss.
HT
TH
HH
TT coulnd't have happened.
I didn't see it till I broke it down in to coin tosses.
We know a coin was tossed twice. We know that heads came up at least once but we don't know on which toss. What are the odds that tails came up on the other toss.
HT
TH
HH
TT coulnd't have happened.
When you are comparing this 2 child family with all other two child families in the world, then it's 2/3.
But logically, I look at it this way:
You know that this guy has two kids.
a=boy
b= boy or girl
All we know about b is that it's either a boy or girl. There is nothing about a that affects the sex of b.
If my logic is flawed, show me how.
Illini:
Can you take a step back and admit that you might be wrong? Go back and reread the original question. The most important part of the question is "we don't know if the boy is the oldest or youngest child". That is the part of the question that I thought had no relevance to the problem but it is the most important when trying to figure out the problem here.
Can you take a step back and admit that you might be wrong? Go back and reread the original question. The most important part of the question is "we don't know if the boy is the oldest or youngest child". That is the part of the question that I thought had no relevance to the problem but it is the most important when trying to figure out the problem here.
I see two conflicting points of logic, and it's fucking with my mind.
On one hand, I know that if you talked to one million dads in this instance, and you knew that they all had two and only two kids, and they all mentioned 1 son, then I know that 2/3 of the rest would be girls.
But at the same time, if a guy walking down the street tells me he has two kids, and one of them is Albert Pujols, why should I assume anything about his other kid?
I'm tired of thinking.
That's a good way of looking at it.
At the risk of being repetitive, I believe this is a simpler way of looking at it than I first posted:
When dealing with probability, we have to look at the total number of possibilities and find out how many possibilities fit the conditions.
What are the only possibilities?
older girl, younger boy: fits
older boy, younger girl: fits
older boy, younger boy: doesn't fit
How many possibilities? 3
How many fit? 2
What is the probability? 2 out of 3
