A contestant on a game show is asked to choose one of three doors. There is a goat behind each of two of the doors, and a car behind the third. The contestant is a goatherder who really wants to win a goat and has no use for a car, living high in rocky hills with no roads. After the contestant chooses one of the doors, the host — who knows where the car is — opens the door the contestant chose and reveals a goat. He then offers the contestant the option to switch doors to one of the unopened doors. Should the contestant switch? Why or why not?