On a game show, you must pick one of two doors. You know that behind each door there is either a new car or a goat. There may be a car behind both doors, a goat behind both doors, or a car behind one door and a goat behind the other. The sign on door I says $"$IN THIS ROOM, THERE IS A CAR, AND IN THE OTHER ROOM THERE IS A GOAT." The sign on door II says $"$IN ONE ROOM THERE IS A CAR, AND IN THE OTHER THERE IS A GOAT." One of the signs is true and the other is false. Which door should you pick, assuming that you would rather have the car than the goat?