The Monty Hall Problem or How to Outsmart a Game Show and Win a Car

The Monty Hall Problem or How to Outsmart a Game Show and Win a Car


Sam Shames
Class of 2014
Massachusetts Institute of Technology

Cameron Tabatabaie
Class of 2014
University of Pittsburgh

Ben Kaloupek
Class of 2014
Northeastern University

Lesson Feedback


This lesson teaches students how to make decisions in the face of uncertainty by using decision trees. It is aimed for high school kids with a minimal background in probability; the students only need to know how to calculate the probability of two uncorrelated events both occurring (ie flipping 2 heads in a row). Over the course of this lesson, students will learn about the role of uncertainty in decision making, how to make and use a decision tree, how to use limiting cases to develop an intuition, and how this applies to everyday life. The video portion is about fifteen minutes, and the whole lesson, including activities, should be completed in about forty-five minutes. Some of the activities call for students to work in pairs, but a larger group is also okay, especially for the discussion centered activities. The required materials for this lesson are envelopes, small prizes, and some things similar in size and shape to the prize.

This lesson has an accompanying animation (animation is currently not availablethat allows students to explore the Monty Hall problem in depth, most likely at home on a computer.

Instructor Biography

Sam Shames is an MIT student, class of 2014, studying Materials Science & Engineering with a minor in Energy Studies. Sam is committed to using Technology- Enabled Education to make residential education more inspiring and engaging. Read more at:

Cameron Tabatabaie is a candidate for an environmental studies degree from the University Of Pittsburgh. He believes education is a core right and need of everyone, and that learning sustains the human spirit, as does helping someone find the passion and the means to do so.

Ben Kaloupek is an Education and Psychology major out of Northeastern University. He believes a learned child is a happy, more actualized child. He hopes that by providing opportunities to learn, we can help a child overcome any obstacle. 

Additional Online Resources

Wolfram Demonstrations Project: Monty Hall
This site, sponsored by Wolfram Demonstrations Project, provides variations on the 3-Door Problem, along with interactive demonstrations of those variations.

Wikipedia: Monty Hall problem
This Wikipedia entry provides a comprehensive history and overview of the Monty Hall Problem.

The New York Times: The Monty Hall Problem
This resource, presented by the New York Times Science Interactive page, provides an interactive educational experience about the Monty Hall Problem, as well as a long article explaining the probability involved.

Real Clear Science: The 'Monty Hall' Problem: Everybody Is Wrong
This article presents an interesting perspective on this classic probability problem.