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So I thought too... having a degree in statistics and all that...Tormuse wrote:Hmm... A math puzzle! I should be able to figure this out...
The answer isn't 50%, but it's not as low as eMTe's guesses either.Well, this is either really easy or really complicated. My first thought is that the person who says yes either has 2 girls or a boy and a girl, so that would make the answer 50%, or half.
No, either of those would be impossible to measure. You could calculate 95% confidence level of how much people I might need to ask before I found a number of people who would answer yes, but for that you would need to know what's the distribution of number of kids a random person has. I'm just asking for the probability of having two girls.If we're asking about the chances relative to the total number of people asked, then my answer gets more complicated.
The probability that the person has two children is 100%, because I already found that person.eMTe wrote:I was thinking along these lines: you need to know if somebody has two children, is one of them a girl and was she born on Sunday. I assumed that maximum number of children one can have is 2 (I don't know why I assumed this, because you didn't set a limit), so a person can have 0, 1 or 2 children - so there's 1/3 probability a person has two children.
That's also 100%, because that person also answered that he or she indeed has a girl born on a Sunday. The only people who come into consideration are people with two children, with the added assumption that one of them is a girl born on a Sunday.Now there's 1/7 chance that at least one of the children was born on Sunday.
Actually, 25%, because it's either boy+boy, boy+girl, girl+boy or girl+girl.Also, if the person has two children - there's 1/3 possibility both are girls - because it can be either boy+boy, boy+girl or girl+girl.
It actually isn't, but our intuition just sucks.But I understand that the puzzle is tricky.
Yes, and that's what we're after. What is the probability that given two children, other which is a girl born on a Sunday that the other child is a girl as well.Tormuse wrote:Sorry, I phrased my question wrong earlier. I know we can't know the total number of people you ask, but generally speaking, in calculating probability, we need to compare the ratio of one particular event to all possible events.
Yes, we're looking after the latter, but with the added information that the other child is a girl born on a Sunday.Are we considering the ratio of families who say yes with two girls to the number of all possible combinations of genders and days? Or are we considering the ratio of families who say yes with two girls to the total number of families who say yes?
This would indeed be the case, but you're forgetting that bit about Sunday.I'm still not sure I'm understanding, but after re-reading the question and looking at your hints, I'm going to guess that you mean the latter, and I now think the answer is 1/3 or 33.3%.
For each person who has two children, you have to consider the gender of each child. They can be boy+boy, boy+girl, girl+boy, or girl+girl. There are four possibilities and three of them have at least one girl. Of those three, only one has two girls. That makes the chance one in three.
No, I deliberately omitted it.Zyx wrote: This would indeed be the case, but you're forgetting that bit about Sunday.
If we're only focusing on the people who answered "yes," and excluding everyone else from our calculations, then the question of what day anyone was born is irrelevant, particularly because of this quote:This seems to suggest that we are only considering the subset of people who said yes to having a family that includes a girl born on Sunday and ignoring everyone else, but...Zyx wrote:That's also 100%, because that person also answered that he or she indeed has a girl born on a SundayNow there's 1/7 chance that at least one of the children was born on Sunday.
this quote suggests that we are *not* ignoring everyone else. This is why I was asking clarifying questions about what we're including in our calculations, because it significantly changes how much work I have to put into my answer.Zyx wrote: This would indeed be the case, but you're forgetting that bit about Sunday.
I'm guessing the Wikipedia page is so long because people are disputing the answer? If that's the case, then you probably got the wording right. It's just one of those questions that people have different opinions on, depending on how you approach it. If the answer is what I think it is, then I'm one of those people who would dispute it and I'll explain why later. I have a feeling I know what information you're looking for now, but this kind of calculation gives me a headache, so I'm going to come back to this later today, when I'm better rested.Zyx wrote: Argh. Now I'm all worried that I worded the original question wrong, but I'm quite sure I have the information gathering in the right order. I really should stop posting puzzles that have longer Wikipedia pages than most western European countries.
?Zyx wrote:births are equally distributed among the week
14 + 14 = 28, but I have to subtract one to get 27, otherwise I would be counting the family with two girls born on Sunday twice. 
After Zyx confirms this, I'll share my other probability related puzzle that this one reminded me of, and then I'll explain why I would dispute the answer. Sure, but where's the fun in that?eMTe wrote:Wouldn't this puzzle sound easier that way?
And that's the correct answer.Tormuse wrote:So, that gets me my final answer: the probability of the family that says "yes" to having a girl born on Sunday having two girls is 13/27. About 48.1%. (Hey, my first answer of 50% was pretty close!)
The original version of this puzzle has two boys and Tuesday, so I mixed it up to make it harder to Google. However, here's the Wikipedia page, and here are good summaries on BBC and ScienceBlogs.I sure hope I got it right this time.
