Question

Ignore what I chose: help w/ a really easy probability problem

Answer 1

Yes, it is better to switch your choice.

At first, you had a 1/3 chance of wining a car.

Then the professor eliminated an option.
Now you are left with either a goat or a car. 

Now instead of having a 1/3 chance, you have a 1/2 chance of selecting the car.

This is famous for the Monty Hall Problem: https://www.youtube.com/watch?v=mhlc7peGlGg