Monty Hall With 100 Doors

There are 100 doors. Behind one door is a car; behind each of the other 99 doors is a goat. You pick one door at random. The host, who knows exactly which door hides the car, then opens 98 of the remaining 99 doors, every one of which reveals a goat. Two doors are now closed: yours and one other. 1. Should you switch to the remaining unopened door? 2. What is the probability you win the car if you switch? What if you stick with your original choice? 3. Generalize: with $n$ doors, the host opens $n - 2$ goat doors. What is your win probability if you switch?