Grades 9-12: Statistics – The Monty Hall Problem (or How to Outsmart a Game Show and Win a Car)


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Content Standards

CCSS.Math.Content.HSS-MD.B.5 (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

CCSS.Math.Content.HSS-MD.B.6 (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Standards for Mathematical Practice

MP1 Make sense of problems and persevere in solving them.

MP3 Construct viable arguments and critique the reasoning of others.

MP4 Model with mathematics.


This lesson titled “Statistics – The Monty Hall Problem (or How to Outsmart a Game Show and Win a Car)” focuses on the Monty Hall problem and teaches students how to make decisions in the face of uncertainty by using decision trees. 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. Some of the activities call for students to work in pairs or groups, especially for the discussion centered activities.


Connecticut teachers should be aware that they would need to include supports for students working above/below grade level, those students who are identified as students with disabilities and for English language learners (ELLs). Connecticut teachers will also want to create and include measures of assessing student learning.


This lesson was chosen due to its rigor and alignment to the Common Core in the area of Statistics and Probability and using probability to make decisions. The lesson also includes clear and sufficient guidelines to support teachers as they teach this lesson. Additional resources, video transcripts and notes are also provided.