The original problem is that there are three doors (2 with goats and 1 with a car behind it). A person chooses one of the three doors then the host picks another with a goat behind it. The person can then choose to pick the other unopened door or stick with his initial choice.
I am given an extension of this problem and I need help with it.
So the question is there are N doors, C cars, D doors that are opened, and G goats where G = N-C
Now I need to find
the probability that the person wins the car given he switches and
the probability that he wins the car given he does not switch
I am not quite sure how to do this. I think Bayes theorem is needed, but I don't know what to do.