lolmaths, I've always found this to be the easiest way to think it through:

1/3 of the time you picked the car. If you change, you get a goat.
1/3 of the time you picked a goat. If you change, you get the car.
1/3 of the time you picked a goat. If you change, you get the car.

So you can see that changing will get you the goat 1/3 of the time and the car 2/3 of the time.


pointless continuation for completion's sake:

1/3 of the time you picked the car. If you hold, you get the car.
1/3 of the time you picked a goat. If you hold, you get a goat.
1/3 of the time you picked a goat. If you hold, you get a goat.

Holding gets you a car 1/3 of the time, and a goat 2/3 of the time.