The Monty Hall problem considers three closed doors, behind one of which is a car and behind the other two of which are goats, you are asked to pick a door and will win whatever is behind it. But before that door is opened, someone who knows what's behind the doors opens one of the other two doors, revealing a goat, and asks you if you wish to change your selection to the third door, that is, the door which neither you picked nor he opened.

Yes. (Assuming you prefer to win a car rather than a goat.)

status | proved in the affirmative

mathematical paradoxes | mathematical problems | solved mathematics problems