Question

(+5)* 7. Uncle Sam puts a dollars in one envelope and 2a in the other. The envelopes are assigned randomly to Alice and Bob. They are allowed to exchange the envelopes after inspecting the content of the envelope they get. Bob observes 10 dollars and computes: with chance 1/2 Alice holds the half of the amount in my envelope, and with chance 1/2 the double of it. Computing the average 5/2+20/2> 10 he is convinced that the exchange is profitable. Alice follows the same line of argument, and they both wish to swap. The exchange, however, seems cannot be advantageous for both. Resolve the "paradox", by explaining what is wrong in their reasoning.

Answer 1

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