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 The Grass is Always Greener II (Posted on 2005-08-11)
In an earlier puzzle, you were handed two envelopes, one of which contained twice as much money as the other. After opening one, you were given the chance to swap. At first glance, it appeared that the your chance of getting more money could only increase each time the envelopes were swapped, but clearly this was nonsense: since there is no probability distribution which allows all real numbers to have the same probability, some values would have to have been more likely than others.

Suppose instead envelopes contain the non-negative integer sums 2n and 2n+1 with probability q(1 − q)n for some fixed q < 1/2

Now of course if the envelope you open contains a 1, you know the other must contain 2, so you ought to swap.

But you can do even better than this. Suppose you open an envelope and find an amount of money 2k

What would the expected value of the second envelope be?

 No Solution Yet Submitted by Sam Rating: 3.8000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 not so sure | Comment 2 of 7 |
well isnt there a possability it coud be less im no mathmatician but it its no paradox the expected value cold be twic as much or half as much.......
 Posted by jeffrey on 2005-08-12 03:46:35

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