Two piece of gold are contained in two same-looking black boxes respectively. It is known that one piece weights twice as the other, but do not know which is which.
Two persons, say A and B, randomly choose a box. One person, say A, opened his box, but he does not known whether it is lighter or weightier.
Question: Is A willing to exchange his box with B?
This might be a well-known problem, but I do not know the proper name to search it online.
Intuitive, it make no difference to exchange the boxes.
On the other hand, if we compute the expectation for A, it seems that A should change the box (the expectation is 1.25 of the current holding).
I would like to hear your answer to the question and preferably fuller story about this paradox.
