Assume you are on a game show, being asked to choose between N doors(N 3). There's a prize behind one of the doors and others are empty. The probability of you choosing the door with the prize behind it is 1/N . Now assume you've chosen a door, but suddenly before opening the door you chose, the host opens N 2 empty doors of the remaining N 1 doors. So now you're left with only 2 unopened doors, the one you chose initially and the remaining one! What is the probability of you winning the prize if you change your decision?

Please compute this probability (e.g. you can use bayes theorem, total probability theorem, conditional probabilities, and such). Please show all work (e.g don't put P(something)=1 without showing work).

The answer should be N-1/N in the end. Need to know how to get there without any lack of work. THank you