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# The Monty Hall ProblemThe Monty Hall Problem

The main mathematical news

1975: Steve Selvin – A solution to Monty Hall Problem. Based upon five assumptions, the odds of winning a car change if you switch your choice of one of three closed doors, once the presenter opened one of the three doors behind which (he knows) there is no car, and lets you reconsider your initial choice.

1990: Marilyn vos Savant replied to a reader of her “Ask Marilyn” column explaining why it is always worthwhile to change the first choice, as this doubles the probability of winning a car from 1/3 to 2/3. This raised a public controversy.

Nowadays, many find it counter intuitive and unbelievable.

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Additional Theorems / conjectures / Open questions

· Changes in one or more of the five basic assumptions, and the implication of such change

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The main mathematical concepts / Principles

MSC2020#97k99; #05D99

Bayes’ Theorem;

Decision tree/Probability tree;

Evenly distributed probabilities;

Extreme case analysis;

Probability, Conditional Probability;

Scenario Analysis;

(Psychology: Action/Inaction Regret, Kahneman and Tversky’s theory);

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