Suppose I have two envelopes full of money and let you choose one. You open your envelope and find X dollars. Then I tell you that one envelope contained exactly twice as much money as the other. You are allowed to either keep the X dollars you have, or switch and keep the money from the second envelope.
It seems switching to the second envelope should be the best bet since it either doubles or halves your current amount of money (you will get 2X or X/2 dollars with equal probability). However your initial choice was arbitrary, so making a switch should not increase your expected outcome. What is wrong?
EDIT: for some good correct solutions see the links people posted below.
It seems switching to the second envelope should be the best bet since it either doubles or halves your current amount of money (you will get 2X or X/2 dollars with equal probability). However your initial choice was arbitrary, so making a switch should not increase your expected outcome. What is wrong?
EDIT: for some good correct solutions see the links people posted below.