Boy or Girl Paradox

Are you sure this wasn't a variant of this problem where one of the result is already known? (Hence the "order" bit). There is a famous problem with endless debate about it, it goes like: a family has two children, one is a girl, what is the probability that the other one is a boy? Depending on the exact wording you can get 2/3 or 1/2.In your case say,A: let two coin flips, one is known to be tails, what's the proba of two tails?B: two coin flips, I show yo

I interpreted it the "wrong" way too. I thought about it like this: Instead of telling me that there is a girl or a boy tell me only that "1 + 1 = 2" and then ask me what the odds of the mothers child are for being a boy. I'll say 50%. I don't care what the state of some other child, I just care what the state of the unknown is. Now, if he had said, "you ask a woman that has a random assortment of children if she has at least 1 girl and she answers 'yes', what are the odds that the other is a bo

Saying "A person has two children, at least one of which is a girl. What is the probability that both of the children are girls?" would more clearly explain the problem.

This intuition is wrong even if turned out to get the right answer. The three unordered options do not have equal probabilities, boy+girl is twice as likely to occur as boy+boy and girl+girl.To get the right answer you must be careful about conditional probabilities (or draw out the sample space explicitly). The crux of the issue is that you are told extra information, which changes your estimate of the probability.(This question as written is very easy to misinterpret. The Monty Hall prob

Looks like this is the Boy or Girl paradox [0], which has ambiguity problems.[0] https://en.wikipedia.org/wiki/Boy_or_Girl_paradox

Take a random parent with two children. You ask them if at least one is a boy and they say yes. The probability that the other is a girl is 66.6%Take another random parent with two children. You ask them if the oldest child is a boy and they say yes. Now the probability that the other is a girl is 50%.This confuses people. (The point is the second scenario gives you more information since it's a subset of the first.)

Take a look at the other replies. I like paxys' for the simplicity.The second ball being selected doesn't change the first event, but it does change our understanding of it.An extreme version: There's a bowl with 3 red and 1 blue balls. We remove two balls again, and the second one is blue. What are the odds that the first one is blue?Your two kids problem is actually pretty complex, in the form you phrased it. Wiki has a decent explanation (I contend that your question i

So it's "what is the probability both are girls?" vs. "what is the probability the other is a girl?" and most people will hear the latter and answer 1/2 whereas the question is the former and its answer is 1/3. Do I have that right?

Is this basically to do with the fact that you know how likely it is to see a boy given any of the combinations? So there's a 33% chance that there are two boys and you see a boy, a 33% chance that there's a boy and girl and you see a boy, and a 33% chance that there's a boy and a girl and you see a girl. Given that you've seen the boy you've eliminated one of the outcomes so the other two outcomes are equally likely?

You're making the mistake he mentions in the article.You're only selecting two child families.Flip one million coins. Select two at random. If one of them is heads, what is the probability that the second coin is heads?