Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He will always eliminate a door that has a goat whether you pick the car or a goat yourself. You, of course, don’t know what is behind your door or the one remaining.  All you know is he eliminated one of the goats. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?  Why or why not?