The Monty Hall Problem

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This activity empowers students to simulate The Monty Hall Problem, a great problem that gets students thinking about probability with minimal background knowledge. To print settings: MakerBot Replicator prints cards with standard resolution and 10% infill. I used TinkerCad to design the cards, starting by drawing pictures of goats and cars. I scanned them, converted to SVG files, and opened them in TinkerCad as holes on a square. Make sure they don't go all the way through to the back, as students will flip the cards over. The Monty Hall Problem is one of probability theory's most famous problems, named after Monty Hall, the host of Let's Make a Deal. A game show contestant chooses one of three doors, with goats behind two and a car behind the third. After choosing, the host opens one of the other doors to reveal a goat. The original door has a 1/3 chance of having the car, while the remaining two doors have a combined 2/3 chance. When the host reveals a goat, the original door's probability remains 1/3, but the remaining probability is transferred to the other door. Begin by explaining The Monty Hall Problem and asking students what they would do in this situation. Give them time to think or discuss with a partner, then take a class poll. Ask one student who stuck and one who switched to explain their choice. Next, have students work in pairs, with one acting as the host and the other as the contestant. The host will be given two goat cards and one car card, which they will place facedown while the contestant looks away. The contestant will choose a card, and the host will turn over a goat. The contestant will decide to stick or switch. Have students run through ten trials, keeping track of their results. Compile everyone's data using an Excel sheet, calculating totals for each column and percentages for sticking and switching. You should see around 2/3 of the time that students won by switching and 1/3 of the time they won by sticking. Materials needed include printed cards with two goats and one car per group. Students will learn about probability in this activity, which can be completed in less than a day.