[tromp]

And then there's this version

> There are two doors with goats and one with a car. You choose one door from the three. The host may select one of the doors with a goat from the remaining two doors, and open it. Should you switch doors if given the chance?

Now the probability can be anything from 0 to 1, depending on what makes the host tick...

Considering the usual ambiguity in the problem formulation, the only safe reply is "It depends".