... the host, Monty Barker, showed her three doors ...
Ok, let me take a stab ...
If you win, you get the car. If you don't get the car, Monty wins.
You can choose 1 door which gives you 1 in 3 chances to win. Therefore, Monty has 2 in 3 chances to win. These odds are established when the rules are set (1 door of the 3 will win). They are not established based on the order in which the doors are opened and they are not re-established after each of the 3 doors are opened.
Therefore, when Carol Merrill (Carol who?) opens one of Monty's doors (not the winning door) after you have selected yours, your chances remain 1 in 3 and Monty's chances remain 2 in 3.
It then follows that if you swapped with Monty, YOUR chances are now 2 in 3 and with only 1 door !!!
Conclusion: Everytime you play this game, make the switch and your odds will double.