About three problems

If the host does not know the car after the door (namely the host will open a door in the remaining two doors, but when the door may be a car, if it is a car, the participants can only win a goat (but this situation does not accord with the experimental requirements), if not a car, the contestants to decide whether to replace option), so participants don't change and change in both cases, the statistical probability of participants selected car, can be analyzed out 1/2. This should be equal to the probability, but how to use code to, please save the children