Mathematician Keith Devlin gave another take on it. Put a mental box around your choice, Door No. 1, and another box around Doors No. 2 and 3 combined. The box around Door No. 1 has a one-third probability associated with it, and the box around Doors No. 2 and 3 has a two-thirds probability associated with it, in terms of containing the car. Now the host opens one of the doors inside the bigger box to reveal a goat. The two-thirds probability of the bigger box shifts to the unopened door. To switch is the correct answer.
