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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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Solution Solution | Comment 43 of 46 |
If X is the smaller amount the other envelope contains 2X
If X is the larger amount the other envelope contains X/2
Thus, the other envelope contains 2X with probability 1/2 and X/2 with probability 1/2.
Thus it results in 5x/4 from

(1/2)2A+(1/2)(A/2)=5/4(A)

The paradox is that X is used in the first term as the smaller amount and in the second term as the larger amount and using both of them in a single formula


  Posted by lost on 2007-02-12 08:36:19
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