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While doing some research on the Bayes Theorem, I stumbled accross the Monty Hall Problem. It goes like this:

Monty Hall was the host of the TV game show, "Let's Make a Deal."

Monty would have a contestant choose one of three doors. Behind two of the doors was a goat. Behind the third was a new car.

Once the contestant made his pick, Monty, who knew which door the car was behind, would open up a door and reveal a goat. He would then give the contestant an opportunity to keep his pick or change it to the other door that had yet to be opened.

The question is: Should the contestant change picks?

The answer is: Yes

The odds of the person initially making the right pick is 1/3. So if he makes the switch, he'll be right 2/3 of the time.

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You forgot a crucial part of the description. If the car is behind the door initially chosen by the contestant, then Monty chooses randomly which door to open between the remaining two doors.

You also didn't explain why the answer that the contestant should switch doors is the correct one (though I'm sure the MH problem has been discussed ad nauseum on this forum).