Monty Hall Problem

Monty Hall invites you to his show. He shows you a fiery red sports car (A Ferrari 360 Spyder!) & two goats. He hides these things behind the doors numbered $1, 2$ & $3$. He now asks you to choose one of these three.

Suppose you choose Door $1$. Now Monty Hall shows you Door $2$. It contains a Goat! He then gives you two choices - stay with Door $1$ or to switch to Door $3$.

If you want to maximize your chances of winning the Ferrari in the long run, what would you choose?

Image Credit : Numberphile