You go on a gameshow where there are 4 doors. Behind 2 doors are cars and behind 2 doors are goats. This is uniformly random. You pick the second door randomly. The host does not open that door. Instead, she is then required to open a door that has a car in it that you did not pick (if there are 2, she does this uniformly randomly). She opens the third door, and you see a car. You now get to open your original door, or switch to one of the remaining doors (you don't get to get the car in the 3rd door). Do you switch or not? Why