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?

This puzzle has echoes of the infamous Monty Hall Paradox. Basically there is a missing "third envelope" in this puzzle. Let's say you are presented with three envelopes. One contains x, and the other two contain x/2. After you pick an envelope, your friend opens one of the envelopes that you didn't pick, and it contains x/2. Now should you switch ? Yes !! See this link for an explanation of the counter-intuitive Monty Hall Paradox:

http://www.comedia.com/hot/monty-answer.html   

Posted by Penny on 2004-05-07 01:06:36