Suppose you're on a game show, and you're given the choice of three doors: behind one door is a sports car; behind all of the others is bicycles. you pick a door, say no. 1, and the host, who knows what's behind the doors, opens another door, say no. 2, revealing a bicycle. he then says to you, "do you want to pick door no. 3? " is it to your advantage to switch your choice?