I just re-read my post and realized that I sounded like a complete ass. Even worse was the fact that I didn't even realize I copied someone else's response. Didn't mean to - sorry. I honestly heard this problem when I was in fifth grade - it was extra credit at the end of some test. I got a Snickers for answering it correctly.

Although the math might be easy - it still screws with all the logic that you have. That's why I love problems like these. It's very similar to the Let's Make a Deal 3 doors problem where logically it makes sense that whether or not you change your door makes no difference, but really you have a 2/3 shot by changing and only 1/3 by keeping your original choice.