The game show that sparked a probability puzzle Host Monty Hall (left) on the set of Let's Make a Deal, the American game show that inspired the famous probability puzzle. The Monty Hall problem asks whether a contestant should switch doors after the host reveals that one of the remaining doors does not contain the prize—an exercise in conditional probability and Bayesian reasoning. (more) Monty Hall problem puzzle Ask the Chatbot a Question More Actions Share Share Share to social media Facebook X URL https://www.britannica.com/topic/Monty-Hall-problem Feedback Corrections? Updates? Omissions? Let us know if you have suggestions to improve this article (requires login). Feedback Type Select a type (Required) Factual Correction Spelling/Grammar Correction Link Correction Additional Information Other Your Feedback Submit Feedback Thank you for your feedback Our editors will review what you’ve submitted and determine whether to revise the article.

　　External Websites Ask the Chatbot a Question Written by Anoushka Pant Anoushka Pant holds a degree in elementary education, with a focus on mathematics, education, and psychology, from Miranda House, University of Delhi. Anoushka Pant Fact-checked by The Editors of Encyclopaedia Britannica Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree.... The Editors of Encyclopaedia Britannica Last Updated: Sep 11, 2025 • Article History Table of Contents Table of Contents Ask the Chatbot { "@context": "https://schema.org", "@type": "FAQPage", "mainEntity": [ { "@type" : "Question", "name" : " What is the Monty Hall problem? ", "acceptedAnswer" : { "@type" : "Answer", "text" : "The Monty Hall problem is a probability puzzle where a contestant chooses one of three doors, one hiding a car and two hiding goats. After a unchosen door is revealed to have a goat, the contestant can stay or switch doors to maximize winning chances." } } , { "@type" : "Question", "name" : " Why does switching doors increase the chances of winning in the Monty Hall problem? ", "acceptedAnswer" : { "@type" : "Answer", "text" : "Switching doors increases the chances of winning to 2/3 because the initial choice has a 1/3 probability of being correct, and Montyu2019s action of revealing a goat provides additional information." } } , { "@type" : "Question", "name" : " How does the Monty Hall problem illustrate conditional probability? ", "acceptedAnswer" : { "@type" : "Answer", "text" : "The problem shows how the likelihood of an event can change with new information. Montyu2019s knowledge and actions affect the probability landscape, demonstrating Bayesian reasoning." } } , { "@type" : "Question", "name" : " What are some cognitive biases related to the Monty Hall problem? ", "acceptedAnswer" : { "@type" : "Answer", "text" : "Cognitive biases related to the Monty Hall problem include counterfactual thinking, illusion of control, and equiprobability bias, which lead people to incorrectly assume that the car is equally likely to be behind either of the two remaining doors or to feel safer sticking with their first choice." } } , { "@type" : "Question", "name" : " How did the Monty Hall problem gain public attention? ", "acceptedAnswer" : { "@type" : "Answer", "text" : "It gained attention when columnist Marilyn vos Savant answered a readeru2019s question in Parade magazine in 1990, explaining that once the host revealed a goat, switching doors gave a better chance of winning. Her answer sparked national debate and controversy." } } ] } Top Questions What is the Monty Hall problem? The Monty Hall problem is a probability puzzle where a contestant chooses one of three doors, one hiding a car and two hiding goats. After a unchosen door is revealed to have a goat, the contestant can stay or switch doors to maximize winning chances.

　　Why does switching doors increase the chances of winning in the Monty Hall problem? Switching doors increases the chances of winning to 2/3 because the initial choice has a 1/3 probability of being correct, and Monty’s action of revealing a goat provides additional information.

　　How does the Monty Hall problem illustrate conditional probability? The problem shows how the likelihood of an event can change with new information. Monty’s knowledge and actions affect the probability landscape, demonstrating Bayesian reasoning.

　　What are some cognitive biases related to the Monty Hall problem? Cognitive biases related to the Monty Hall problem include counterfactual thinking, illusion of control, and equiprobability bias, which lead people to incorrectly assume that the car is equally likely to be behind either of the two remaining doors or to feel safer sticking with their first choice.

　　How did the Monty Hall problem gain public attention? It gained attention when columnist Marilyn vos Savant answered a reader’s question in Parade magazine in 1990, explaining that once the host revealed a goat, switching doors gave a better chance of winning. Her answer sparked national debate and controversy.

　　Imagine you are a contestant on a game show. You are presented with three closed doors. Behind one is a car—the prize you want. Behind the other two are goats. You choose one door, but it remains closed. Now the host—who knows what is behind each door—opens one of the other two doors, revealing a goat. You are then offered a choice: Which option would you choose to maximize your chances of winning the car? This is the Monty Hall problem, a probability puzzle named after Monty Hall, the host of the American television game show Let’s Make a Deal ...(100 of 850 words)

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