The Car-and-Goats II
This is a continuation of the previous question... If the car is actually at Door I (probability 1/3), then when you switch you lose; but if it is at Door 2 or Door 3(probability 2/3) then the host's revelation of a goat shows you how to switch and win. Therefore the chance you win by switching is 2/3. Elegant. But in this argument, we are still considering the possibility that the car is behind Door 3; so the host cannot have already opened the door (much less to reveal a goat). In this game, you have to announce before a door has been opened whether you intend to switch.