One of my all-time favorite problems:
I have two boxes. Each has some positive amount of money in it, but I will give you no information about the possible dollar amounts other than the fact that one box has exactly twice the amount of money in it as the other. You randomly select one of the two boxes, open it, and find $100 inside. I now give you the option of keeping the $100 or switching boxes with me and keeping whatever’s inside the other box. Which should you choose?
If you’d like a related problem that might help you think about this differently, click below.