In article <firstname.lastname@example.org>, Ray Vickson <RGVickson@shaw.ca> wrote:
> On Mar 11, 6:56 pm, Steven <sgottlie...@hotmail.com> wrote: > > Suppose you meet me on a street corner and I introduce you to my son who is > > with me. I inform you that I have another child at home. What is the > > probability that my other child is a girl. > > I looked at the sample space which I claim is bb, bg, gb and so the answer > > is 2/3. Is this correct? > > Steven > > Yes, provided that you don't say which child is older. If you do say > which is older, the probability becomes 1/2! You can also look at the > problem this way: you toss a coin twice and announce that you got at > least one Head. What is the probability the other outcome was a Tail?
"Other" is not well-defined in this coin experiment, but it is in the OP's problem. I think your coin example models the following: You meet me on the corner, I tell you I have two kids at home, you ask if they're both girls, and I say no. Then the probability is 2/3 that I have a daughter. But if I'm out with one of my two kids, who's a boy, then the probability my other kid is a girl is 1/2 - assuming I'm equally likely to have my other kid with me. I think this is a better model for the OP's problem. The coin problem analogous to this is: I have two coins, I toss each, then randomly choose the result of one of the tosses to announce. If I say heads, what is the probability the other toss is tails?
> Again, the probability that the other outcome is a Tail is 2/3 if you > don't say whether your announced Head was first or second, and is 1/2 > if you do announce its position. > > R.G. Vickson