Hey Khetu! So I am going to take the easy path and say that both approaches are correct. The reason i say so is because I think that the answer depends on how you treat the question. If you treat this a Bayesian problem to find the other given the prior, then 1/3rd is the correct answer. But I also agree that in the case of gender, there is no dependence of the first on the other. Therefore, my initial answer was 1/2. But I did find merit in looking at it from a Bayesian perspective to arrive at 1/3. I did look this up, and apparently this a paradox where people remain divided on the correct answer. See here: https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
First of all, thanks for spending so much time on this - I am just obsessed with this simply because probability and nowadays Bayesian probability is the foundation stone of statistical inferences but we all still have problems with a very basic probability problem.
I had written a long reply to this but after hitting "post" it asked me to log back in and the comment was gone. So now I will keep it short - after reading the Wikipedia article, I realize that the problem is indeed paradoxical. It all boils down to sample space. If your sample space is {BB, BG, GB}, then you answer will be 1/3. And if your sample space is {B,G} since you do not take into account the child you already know is a boy, then the answer is 1/2.
I think the man wasted the time.Time is precious than money
I disagree with the answer to the 2 girls probability problem and I had written a blog post about it in 2009 where it was 2 bears and not 2 girls but the same mathematical dilemma - http://salilkhetani.blogspot.com/2009/08/conditional-probability-2-bears.html
Hey Khetu! So I am going to take the easy path and say that both approaches are correct. The reason i say so is because I think that the answer depends on how you treat the question. If you treat this a Bayesian problem to find the other given the prior, then 1/3rd is the correct answer. But I also agree that in the case of gender, there is no dependence of the first on the other. Therefore, my initial answer was 1/2. But I did find merit in looking at it from a Bayesian perspective to arrive at 1/3. I did look this up, and apparently this a paradox where people remain divided on the correct answer. See here: https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
First of all, thanks for spending so much time on this - I am just obsessed with this simply because probability and nowadays Bayesian probability is the foundation stone of statistical inferences but we all still have problems with a very basic probability problem.
I had written a long reply to this but after hitting "post" it asked me to log back in and the comment was gone. So now I will keep it short - after reading the Wikipedia article, I realize that the problem is indeed paradoxical. It all boils down to sample space. If your sample space is {BB, BG, GB}, then you answer will be 1/3. And if your sample space is {B,G} since you do not take into account the child you already know is a boy, then the answer is 1/2.
Sorry I had missed your revert. Let me come back to you over the weekend on this.