Question: Monty Hall (the host of Lees Make a Deal) has presented Fred with the choice of three doors. Behind two of the doors are "booby prizes." A new car is behind the other door. Fred selects a door (#1, for example). Monty then shows him a booby prize behind one of the unselected doors (#2, for example). Monty then, offers Fred the chance to switch from his original selection to the unopened, unselected door (#3 in our example). Should Fred switch? (Aside: This is a very famous problem and was the subject of a front-page New York Times article some years back.)