"Let's make a deal" problem

[BulletsBlitz]

This question was posed recently by my statistics instructor. I am curious to see how much a part of conventional wisdom it is.

Lets say you are on the 1970's game show Lets Make a Deal. You reach the segment of the game where you are asked to pick one of three doors. Behind one of the doors is a wonderful prize like a new car. Behind the other two doors are gag prizes such as a can of dog food or a billy goat.

After you choose, the host will always open one of the other two doors and reveal a gag prize. He then will give you the option to stick with your original choice or switch to the other unopened door.

To give yourself the best chance of winning the grand prize, should you:

A) always stick with your first choice.

B) always switch to the other door.

C) it makes no difference, there is an equal probability that either door is the winner.

Please explain why you selected your choice