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The grass is always greener... (Posted on 2004-05-06) Difficulty: 3 of 5
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?

No Solution Yet Submitted by Gamer    
Rating: 3.8824 (17 votes)

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Sorry, not Perplexed........:) Comment 46 of 46 |
How does taking the average value for both of the envelopes mean that only the 'other' envelope will average 5/4x in value.  Not only will the other envelope's average value be 5/4x, but the average value of the chosen envelope will also be this.  To be honest, I can't see the paradox in this problem.
  Posted by John zadeh on 2007-06-25 22:12:13
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