Based on the information provided, it would be to your advantage to switch your choice. Let me explain:
- Originally there was a 1/3 chance the car was behind your chosen door #3
- When the host opened door #2 to reveal a goat, that means the car must now be either behind your original choice of door #3 or the remaining unopened door #1
- So now there is a 1/2 chance the car is behind door #1 if you switch
- By sticking with your original choice of door #3, there remains only a 1/3 chance of winning the car
- Therefore, by switching your choice to the remaining closed door #1, you increase your chances of winning the car from