Probabilities...

One of the simplest probability tests, but one where several people get it wrong:

In a quiz-show from USA, the participants got to choose one of three doors. Behind one of the doors was a brand new shiny car, behind the other two were goats.

After the participant had chosen one door, but without that door had been opened, the host open one of the other, showing a goat. Now the participants could choose again, either to stick with their first choice, or swith to the other of the closed doors. The door that is opened has obviously a goat as a prize...

After the participant had made this other choice (to stick with the first door or to change), the host opens the dchosen oor, revealing the prize... with hope a car.

Now the question is:
What is best from a probability standpoint, to stick with the first choice of door, or to change door when you have the chance?

/Sebastian