Experimenting on Humans
The subject of the experiment, whom we will refer to as “Chris” was privy to all the details of the experiment in advance, and participated willingly.
One Sunday evening, Chris went to sleep at the observation labs. In another part of the lab a fair coin-toss was conducted, yielding a result of heads or tails. Chris was aware that the coin-toss was made, but not the results of the toss. However, he was made aware that the following events would transpire, dependent on the results of the toss:
If the toss came up heads, Chris would be awoken at 6AM on Monday morning and asked what the probability was that the coin had come up heads.
If the toss came up tails, Chris Would be awoken at 6AM on Monday morning and asked what the probability was that the coin had come up heads. BUT, on Monday evening he would be given an amnestic, putting him to sleep and totally clearing his memory of the previous 24 hours. Then, on Tuesday morning he would be awoken at 6AM and asked what the probability was that the coin had come up heads.
The amnestic had no side effects other than removing the previous days memories and resetting his body’s internal clock back 24 hours. Upon awaking, Chris had no certain way of knowing whether the amnestic had been administered, or what day it was.
Now would we answer 1 in 2, or 1 in 3 if we were in Chris’s place? And why….
(I believe this puzzle to be by an MIT graduate student named Adam Elga.)