Consider an experiment in which a volunteer subject is told the following
by the experimenter:
"You will be given a sleeping pill. After you are asleep, I will flip a
fair coin. If the the coin lands head up, I will make an exact duplicate
of you, place you and your clone in seperate identical rooms, and wake
both of you up. Neither of you will be able to tell whether you are an
original or a clone. Then I will ask both of you the following questions
1. What is the probability that you are a clone?
2. What is the probability that the coin landed head up?
If the coin lands tail up, I will place you into one of the rooms
mentioned above without making a copy of you, wake you up, and ask you the
same questions. Also in both cases the the original (non-clone) is also
asked a third question
3. You are not a clone. What is the probability that the coin landed head
up?"
It seems to me that there are two possible sets of correct answers.
A. 1) 1/4, 2) 1/2, 3) 1/3
B. 1) 1/3, 2) 2/3, 3) 1/2
I personally prefer answer set B. I have some justifications, but they are
not terribly convincing. I can try to spell them out, but first I wonder
if anyone else has thought about similar problems.