Most people can readily understand that since you selected one of the three doors, if you stay, the probability of winning is 1/3. What happens if you switch? Assuming that the host always opens a door that does not have the car, and this is a crucial assumption, you have a 2/3 chance of winning if you switch.There are three equally likely possible orderings of the prizes behind the three doors, shown as A, B, or C.

Suppose the player has selected Door 1. If the car is behind Door 1, as in order A, the host will open either Door 2 or Door 3, and if the participant switches, he or she will get a goat. If the car is not behind Door 1, as in order B or C, then the host will open the remaining door that has a goat, and if the player switches, he or she will get the car. Only order A would result in a loss, that is, a goat. This same analogy also works if you start with the player selecting Door 2 or Door 3. The probability that player wins a car with a switch is . = 2/3