Consider this example: A player in a game show was asked to choose between three doors, two doors contain a faulty prize, while the other contains a million dollars. As the player wanted the money, he chose one (in this case, the probability of choosing the door with the money is 33.33%). Since the host knows where the prize money is, he opened one of the doors with a faulty prize. The player is then asked if he wants to switch doors. According to the solution of the problem, it is more likely to have the prize money if the player were to switch doors (66.66%). Here is my problem: If, before the player decides to switch doors, the player received urgent news and was permitted to leave the game show. His brother, who wasn't paying attention to the game, came as his replacement. The host asked him to choose between the two available doors, where one of them contains the prize money. (I couldn't think of a better example :P) Now, doesn't the probability of acquiring the money is 50%, which contradicts the 66.66%? Which of the two probabilities is correct? I have been thinking that there might be physical systems with similar situations (like a system where we thought of just having two possible states but actually contains three).