3. A game show involves three doors. One door conceals a brand new car, and the other two doors conceal rubber chickens. To start the game, the contestant picks one of the doors. The host then opens one of the other doors, revealing a rubber chicken. Finally, the contestant is given the option to either open the door they have chosen, or switch and open the other door. Using the Law of Total Probability, explain why the contestant will double their chances of winning the car if they switch doors.

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