Monty Hall, Three Doors
Exploration Questions

The game simulates a well-known game show situation that used to happen on the Monty Hall game show. A player is given the choice of three doors. Behind one door is the Grand Prize (a car and a cruise); behind the other two doors, booby prizes (pigs). The player picks a door, and the host peeks behind the doors and opens one of the rest of the doors. There is a booby prize behind the open door. The host offers the player either to stay with the door that was chosen at the beginning, or to switch to the remaining closed door.

Try to predict what is better: to switch doors or to stay with the original choice. What are the chances of winning in either case? Play the game many times and see if the experiment confirms your prediction.