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Visualizing The Monty Hall Problem

A clear diagram to help you understand this counter-intuitive solution

Cole Frederick
Science Spectrum
5 min readDec 24, 2024

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Of the three doors, only one holds the prize (Source)

The Monty Hall problem has become one of the most popular mathematical puzzles. This is due to its simple structure but an odd solution. The problem statement easily fits into a few sentences. I first heard about this puzzle in the show Brooklyn 99 (one of my absolute favorite shows!). Two of the characters are engaged in an intense debate about what the correct choice is. This problem is also featured in several other movies and shows, like Mythbusters and 21.

Monty Hall, the host of Let’s Make A Deal, featured a similar puzzle on his show (Source)

The premise is simple. Imagine that you are on a game show, and there are three doors in front of you. One of them has a car behind it, and the other two have goats. The goal is to select the door with a car. You can select any of the three doors, and they all look the same. After you make your choice, the host will open one of the two remaining doors, and it will always have a goat behind it. You are then given the option to pick the remaining door or keep your original one.

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Science Spectrum
Science Spectrum

Published in Science Spectrum

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Cole Frederick
Cole Frederick

Written by Cole Frederick

Ph.D. Candidate in climate science | Editor of Science Spectrum

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