For those of you with maybe 10 minutes of spare time, it is fairly easy to convince yourself of the correct answer.

Grab a volunteer, three plastic cups and a cotton ball. Have the cotton ball represent the car, and the other empty cups the goats. Have your volunteer turn away while you place the cotton ball under a cup. Have the volunteer first switch all the time, for maybe 20-30 trials, and then stay every time for 20-30 trials. I did a science fair project on the subject once and my results were as follows:

Switching for 1000 trials: 664 wins, 336 losses

Staying for 1000 trials: 332 wins, 668 losses

jman_red