You are told there are two envelopes. One contains twice as much money as the other one. You pick one but are allowed to change your mind after picking it. (You are equally likely to pick the one with less money as the one with more money.)
To figure out how much on average the other envelope should contain, one might average x/2 and 2x because one is equally likely to pick one as picking the other. Since this comes out to 5x/4, one might always change his or her mind. But wouldn't this end up with one never making up his or her mind?
Suppose you pick Envelope 1, and it contains x.
Envelope 2 either has 2x, or x/2. Supposing you change your mind, and choose Envelope 2, one case yields x profit, while the other yields -x/2 profit.
Since you could potentially gain twice the amount you could potentially lose, shouldn't you always switch?
Posted by Dustin
on 2004-10-31 00:05:14