In a TV game show a candidate is given the following problem. Three rooms are closed
by three identical doors. One room contains a luxury car, the other two each contain a
goat. The candidate is asked to guess behind which of the doors the car is. He chooses a
door which we will call "A". The door "A", however, remains closed for the moment. Of
course, behind at least one of the other doors there is a goat. The quiz master now opens
one door which we will call "B" to reveal a goat. He now gives the candidate the chance
to either stay with the original choice "A" or to choose remaining closed door "C". Can the
candidate increase his or her chances by choosing "C" instead of "A"? Prove your answer.
