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?
Assume that the difference between the two envelopes is d. Then, d is also the value of the envelope with the lesser amount of money.
So when you choose an envelope and you decide to switch:
If you switch from the lower to the higher amount, you gain d.
If you switch from the higher to the lower amount, you lose d.
So, you are actually stand to win the same amount that you stand to lose, and it doesn't matter if you switch or not.
Posted by Joe
on 2005-11-06 18:11:25