College Algebra Related Pages: 625 extension of "Using the Complement in a Probability Problem"
College Algebra and Trigonometry Related Pages: 917 extension of "Using the Complement in a Probability Problem"
Precalculus Related Pages: 839 extension of "Using the Complement in a Probability Problem"

Monty Hall was originally a TV game show in the 1960's. Studying the game from the aspect of probability yields interesting and somewhat unexpected results. In this game you are studying the probability of winning the prize behind one of three doors. Initially, you choose a door and then another loosing door opens. At this point you decide to either stay with the door you first picked or switch to the other unopened door.

To understand why the probabilities of this activity turn out like they do it is necessary to understand the complement of an event. Initially, the probability that the prize is behind one of the doors is 1. The probability the prize is behind the door you choose is 1/3. The probability the prize is behind one of the other doors is the complement, or 1 - (1/3). After you have chosen a door another door opens. The probability that the prize is behind the other unopened door must still be the complement because the prize is not behind the door which just opened. Therefore the probabilities will always be on your side if you switch doors.

Run the applet many times. Keep track of the statistics and you will see the probability of winning upon switching will approach the complement, 1 - (1/3) = 2/3 !