 The conditional probability of winning by switching is , which is .The conditional probability table below shows how 300 cases, in all of which the player initially chooses door 1, would be split up, on average, according to the location of the car and the choice of door to open by the host.Many probability text books and articles in the field of probability theory derive the conditional probability solution through a formal application of Bayes' theorem; among them Gill, 2002 and Henze, 1997.