I posted a similar problem on here a couple of years ago, if you
remember that don't contribute, just sit back and enjoy the discussions!

I phone a work colleague up and his daughter answers the phone. He has
previously told me that he has two children at home, I had no idea he had
a daughter. What are the chances that the other child is also a girl?

Originally posted by wolfgang59 I posted a similar problem on here a couple of years ago, if you
remember that don't contribute, just sit back and enjoy the discussions!

I phone a work colleague up and his daughter answers the phone. He has
previously told me that he has two children at home, I had no idea he had
a daughter. What are the chances that the other child is also a girl?

I'm going to stick my neck out here and say the probability is 1/3?

Let's take an infinite set of families with two children, where children have an equal probability of being boys or girls, and you ask the question:

"Of all of the families with at least one girl, what is the probability that both children in that family are girls?"

Then the answer is 1/3

If, on the other hand, you randomly choose one family, and then randomly sample one of the children, and discover that child is a girl, then the probability that the other child is a girl is not conditionally related to your sample and the probability is 1/2.

Of course if you phone the work colleague up somewhere that is not his home it could be one of his 5 children that have left home.

If you have four two children families BB, BG, GB, GG. You take a random sample of one by for instance phone. There is only one case in which the other child matches your sample (and one case which is clearly excluded by the result of the sample). So I am still sticking with 1/3.

Originally posted by deriver69 Of course if you phone the work colleague up somewhere that is not his home it could be one of his 5 children that have left home.

If you have four two children families BB, BG, GB, GG. You take a random sample of one by for instance phone. There is only one case in which the other child matches your sample (and one case which is clearly excluded by the result of the sample). So I am still sticking with 1/3.

1/3 is incorrect. Think again.

In fact it may help to consider the same problem ... but with gender reversed!