Writings - Minor documents

A very well known problem of probability theory is presented below:

Person P is the winner of a competition and is therefore allowed to compete for a car. The compere introduces P to three doors, labelled A, B, and C, respectively. Behind two of the doors, there are merely cheap toys to be found, but behind one of the doors, a grand new car is waiting for a new owner. Person P is to choose one of the doors, and will be given whatever is found behind it. P chooses door A. After that, the compere unexpectedly opens one of the remaining doors, B, hiding a toy. Then, Person P is given the choice to change to door C. In order to obtain as high probability as possible of winning the car, should Person P change to door C or stick to door A?

This document containes a theoretical discussion.