A contestant on a quiz show is asked to choose one of three doors. Behind one of the doors is the star prize of a sports car, but behind each of the other two doors there is a toy car.
The contestant chooses one of the three doors.
The host then opens one of the remaining two doors and reveals a toy car. The host then asks the contestant if they want to stick with their first choice or switch to the other unopened door.
State what you would recommend the contestant to do in order to have the greatest probability of winning the sports car. Show your working clearly.