this is actually an old problem solved by vos Savant, and I can't get to the bottom of it. It goes like this:
A shopkeeper says she has two new baby beagles to show you, but she doesn't know whether they're male, female, or a pair. You tell her that you want only a male, and she telephones the fellow who's giving them a bath. "Is at least one a male?" she asks him. "Yes!" she informs you with a smile. What is the probability that the other one is a male?
Savant replied "one out of three".
I convinced myself pretty hard that the answer should be 2/3, so I'm looking for explanation of Savant's answer.
If at least one is a male, and you have 2 puppies, one yellow and one green collar, there are 3 possible combinations (I agree with her so far):
YM & GM
YM & GF
YF & GM
So, if you choose Y collar, there is 2/3 chances, that the other one is a male, and of course the same for G collar.
Where did I get it wrong?