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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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Strange... | Comment 20 of 46 |

You are equally likely to choose the greater amount as the lesser, but can change your mind after picking. Changing your mind would not solve the problem of chance unless you took upon data from the envelopes, such as weight and structural feel. The one with the greater amount would obviously be thicker; unless, they both had checks inside, then you would be screwed.

The choice presents a set of an infinite number of elements; however, you could change your mind a hundred thousand times and still be faced with the 50/50 chance of choosing the envelope with the greater amount.

Yea, you'd never make up your mind if you were looking for some sort of justification for choosing an envelope.

The amount inside the envelope is irrelevant unless you know how much is inside them, and even in that situation, that amount is irrelevant to making a decision on which envelope to choose. Even if you knew what amounts were in each envelope, you still have a 50/50 chance of choosing the right one no matter how you work the math.

Is this a math problem or a strange attempt at psychology? I don't understand what's trying to be solved.

  Posted by Balance on 2004-08-12 00:54:48
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