Originally posted by Instant Access:
The question says that I got to choose a bottle. I picked a good bottle.
Let's physically remove that wine from the set.
I am looking at one other bottle of wine in my set. Either it's (1) A or B (it can't be both) or (2) it's D.
That's precisely where the problem lies, you don't know if it is A or B if it came from the good set where as you KNOW it is C if it came from the bad set.
As for the B/G question think of this way, I have a one year old and a two year old. They are two distinct individuals. Let XY denote the pair of sexes for the two kids where X is the sex of the one year old and Y is the sex of the two year old. There are 4 possibilities (BB, BG, GB, GG). You cannot argue that BG and GB are the same because in the former that means my one year old is a boy and the latter the one year old is a girl. (I don't have kids but if I did I wouldn't want ones that can change sex!
) So when I tell you that at least one of them is a boy, you cannot disregard that all you know is (BB, BG, GB) are the possibilities. Again, BG is not equal to GB.
This is the same with the wine example. Let's say that XY is the lot you chose and X is the bottle you sampled. Now let's literally write the letters ABCDEF on the bottles and then brown bag them. Now you taste a good wine, this means you have tasted either A, B, or C. Now the problem is, if you want the answer to be 1/2 you are thinking the following. If it is A or B I am tasting, I will remove the brown bag. If it is C I won't. So without removing the brown bag (and we don't in the original problem), you could be holding AB, BA, or CD. I agree that AB is the same as BA, but only if you knew whether you tasted A or B (which is not what we assumed since the brown bags are still on).