1 Probability (10 points) Assume you are a contestant of a game show in which you are presented with three closed doors. Behind one of the doors is a car which will be yours if you choose the right door. After you have randomly (as you have no prior information) selected a door, the game host opens one of the other two doors which has nothing inside, while keeping the rest of doors closed. The host then asks whether you want to stay with your original selection or switch to another door. Should you change? Calculate the relevant posterior probabilities to explain your choice