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?
As it is mentioned that there is equal chance for each, and an average of 5/4x for each, then surely the best way would be to simply pick one at random, and the chance is the same for both, and no information is presented to indicate which would have the most money in. It is like thinking of the colour of a box that you can't even see. There is no way to work it out.
Posted by Jake
on 2004-07-16 09:04:46