While we're on the subject of probability, how about one of the most controversial problems in Mathematics, one that has caught out even professional mathematicians.
You are on a game show. The compere shows you three doors. Behind one door is a brand new car, behind two of the other doors are goats. You choose a door. The compere then opens one of the other two doors, to reveal a goat behind it. He then asks you if you want to stick with your original choice, or switch to the other remaining closed door.
Do you improve your chances (of getting the car) by switching to the other door?