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The Monty Hall Problem

How it works

Based off the famous problem from the game show Let’s Make a Deal (whose host was named Monty Hall), students are presented with three cups where one of the three contains a prize, and the other two are duds. The player starts by selecting the cup which they believe holds the prize, then the host removes one of the remaining cups which does not contain the prize. After that, the host gives the player the option of staying with their original guess or switching their choice to the last remaining cup. After the player makes their choice, the host reveals to everyone which cup holds the prize.

Three Cup Game rules handout
Frequency graphs handout
Questions and six cup handout
Video example of Three Cup Game

Why we like this activity:

  • It’s fun! Students have a lot of fun with the game show environment.

  • It helps to develop probabilistic intuition and reasoning.

  • It encourages data collection and visualization.

  • It requires students to engage in mathematical habits of mind:

    • Making observations / looking for patterns / making and testing predictions / understanding and explaining when trying to figure out whether you’re more likely to get the prize if you stick with the same cup or switch to a different cup.

    • Finding similarities and differences between the three cup game and the six cup game.

To find out more about our approach to math and math education, click here.