==Conditional version of the problem== 

 ==Some possible observation== 

 ===A - The door hiding the car is independent of the door initially chosen by the player=== 

 ===B - The event that the car is behind the originally chosen door is independent of the door opened by the host=== 

 ===C - There is a symmetry with respect to door numbers=== 
 The door numbers can be arbitrarily rearranged at the start of the game without changing any probabilities. 

 ==Simple solutions==