Consider this scenario:
You have almost won at a game show! Your host, Monty, gives you one final task. He lifts the curtains to reveal three closed doors, labeled A, B, and C. He informs you that behind the doors, in some order, there are two goats and a grand prize. The doors are identical and there is no way to tell what is behind them. He asks you to pick a door, which you do, picking one at random (let’s say A). Monty turns around and, in a fit of generosity, tells you that he will help you out by opening one of the unselected doors that contains a goat (let’s say B). Having taken one of the doors out of the running, he now gives you a choice. “Would you like to switch your selection to C or stay with A?”, he asks.
As you stand there, what should you do to have the best chance of winning the grand prize? Is there a systematic way to find out?