### Monty Hall Experiment

Door 1 Door 2 Door 3
Distribution graph

#### Description

In the Monty Hall experiment, there are three doors; a car is behind one and goats are behind the other two. The player selects a door and then the host opens one of the other two doors. The player can then stay with her original selection or switch to the remaining unopened door. The door finally selected by the player is opened and she either wins (the car) or loses (with a goat).

Either of two host strategies can be selected with the list box. In the standard strategy, the host always opens a door with a goat); in the blind strategy, the host randomly opens one of the two doors available to him. The player switches doors with probability $$p$$, a parameter that can be varied with the input control. Random variable $$U$$ is the number of the door with the car; $$X$$ is the number of the first door selected by the player; $$V$$ is the number of the door opened by the host; and $$Y$$ is the number of the second door selected by the player. Random variable $$W$$ indicates a win: $$Y = U$$. The variables are recorded in the record table on each update.

The probability density function of $$W$$ is shown in blue the distribution graph and is recorded in the distribution table. On each update, the empirical density function of $$W$$ is shown in red in the distribution graph and is recorded in the distribution table.