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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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No Subject | Comment 45 of 46 |

We can't have 5x/4 or 1.25x.

That would be a classic case of confusing variables for constants.

In one case, switching gets x/2, in the other case, switching gets 2x, but x is different in the 2 cases. So, we cannot simply average the 2 different x's to get 5x/4. We can average the 2 amounts, to get the expected value of switching, which is also the expected value of not switching, but we cannot under any circumstances average x/2 and 2x.


  Posted by Jean-Louis on 2007-04-11 00:43:57
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