# The Monty Hall Problem

*Audience*: Beginning programming students

## Objectives

- Students will learn the value of thinking a problem through before they program
- Students will learn that the obvious answer is often wrong

## Exercise

The Monty Hall problem is
based on the old TV game show *Let’s Make a Deal*. In that show, the
moderator, Monty Hall, would select a member of the audience, and offer them
a valuable prize. The prize was behind one of three doors. Behind the other
two were joke prizes, like a goat and a can of paint. The member of the
audience would select one of the doors (say, door number 2). Monty would
then say, “Before I show you whatÕs behind door number 2, let me show you
what’s behind door number 1.” Door number 1 would open, to show the can of
paint. Then Monty would ask if the player wanted to change to a different
door. The question is, should the player do so?

Write a program to simulate 100,000 iterations of the Monty Hall problem.
Use the simulation to demonstrate whether it is to the player’s advantage
to change doors.

## Discussion questions

- Do you think the simulation is accurate, based on the results? Why or why not?
- What is the
*minimum* number of lines of code to do the simulation?