Monty Hall Paradox in Probability

There are three closed doors, two with goats behind them and one with a car. You win what is behind the door that you choose. After you select a door, the game show host opens some other door and shows you that it has a goat. You are then given the choice of changing your choice of door. Should you alter your decision? Most people would stick to their original choice, but it turns out that you can double your chances of winning the car by changing doors.