Jan Poland → Math fun → Two Envelopes  

The Two Envelopes Paradox Suppose someone shows you two closed envelopes containing money and proposes you the following game.
Question: Should you change or not? Naive answer: The setting is symmetric, and knowing the amount in the first envelope does not give you any hint. So it does not matter if you change or not. Refutation: After having observed the first amount x, the probability that the second envelope contains twice as much is one half. Therefore, if you change your choice, with probability 0.5 you gain x, while with probability 0.5 you loose x/2. Therefore you should change. What do you think? Want to read my extended solution? 



Disclaimer  Last update: Fri Mar 9 05:09:33 2007 GMT by Jan Poland, Page = "Two Envelopes" 