Mathematical Paradoxes: The Monty Hall problem

It has been some time since the first mathematical “paradox” I posted: the twin coin flipping which generated lots of discussion and controversy! So, with no further delay, I am moving on to another classic: the Monty Hall problem.

In a reality show you are presented with three doors Red, Green, and Blue. One of the doors contains one million dollars as a prize! Let us say you choose the Red door. The presenter will not open the door immediately. Instead the presenter (who knows where the prize is) must first open one of the other two doors, Green or Blue, but not the one with the prize (in case the one you picked doesn’t contain the prize). So, he opens the Green door and there is no prize behind it. He then asks if you would like to change your original selection (Red door) and choose the Blue door instead. What do you do? Do you stick to your initial selection (the Red door) or do you change for the Blue one?