Monte Hall Problem. Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. After you pick a door, say No. 1, the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to switch to the other door (in this case No. 2)?" Is it to your advantage to switch your choice? Here are the rules of the game:
1) You must pick a door (1,2 or 3).
2) The host must always open a door that was not picked by the contestant.
3) The host must always open a door to reveal a goat and never the car.
4) The host must always offer the chance to switch between the originally chosen door and the remaining closed door.
Create a decision tree to show whether switching your choice to the other closed door is a wise decision.