Here's the Proof

Further to my post about ‘Monty Hall problem’ where you're given a choice of three doors, and having chosen one door the host opens one of the other doors without the car. The question now was, do you now switch to the other unopened door to improve your chances of winning?

Assuming the car is behind door B, here's a probability diagram I drew of all possible outcomes:


We can see that when the contestant switches the chances of winning are two thirds, whereas when he doesn't switch the chances of winning are only one third.