I'm in a class titled "Puzzle Based Learning" and we were given this problem:
There is a new game show and you are the participant. There are two doors, each has a suitcase with gold coins behind it. You know that these suitcases contain amounts from the set: 25, 50, 100, 200, 400, 800, 1,600, 3,200, and 6,400. You also know that one suitcase has twice as much coins as the other. You select the door and open the suitcase. You find 1,600 gold coins. Then the game show host offers you the opportunity to switch doors. Do you do it? Justify your answer.
In class, the professor tells us:
The two possibilities of the suitcase are 800 and 3200. The expected outcome of choosing one suitcase would be 800*.5 + 3200*.5 = 2000. Since 2000>1600, you should choose again because the expected outcome is greater than 1,600.
I was hoping someone could explain this a little more clearly. In my mind, it seems there is a 50/50 chance of getting 800 and 3200 and the "expected outcome" is meaningless because we shouldn't care about the payoff of choosing again. You have a 50% chance of losing.
Am I missing something? Is this a trick question? Is my professor pulling my leg?