User:Martin Hogbin/MHP - Economist

The analysis can be illustrated in terms of the equally likely events that the player has initially chosen the car, goat A, or goat B (Economist 1999):

1.

Host reveals
either goat

Player picks car
(probability 1/3)

Switching loses.

2.

Host must
reveal Goat B

Player picks Goat A
(probability 1/3)

Switching wins.

3.

Host must
reveal Goat A

Player picks Goat B
(probability 1/3)

Switching wins.

The player has an equal chance of initially selecting the car, Goat A, or Goat B. Switching results in a win 2/3 of the time.