Monty Hall for N doors: You are a contestant at a show with N closed doors where N > 3. One of the doors has a car and all the others have no prize. You first pick a door at random. Then, the host picks a door uniformly at random among the remaining doors that have no prize in them and opens that door for you. You then face the choice of sticking with your initial selection or switching to one of the remaining closed doors uniformly at random? How should you play? Justify your answer with rigorous probability calculations.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Monty Hall for N doors: You are a contestant at a show with N closed doors where N > 3. One of the doors has a car and all the others have no prize. You first pick a door at random. Then, the host picks a door uniformly at random among the remaining doors that have no prize in them and opens that door for you. You then face the choice of sticking with your initial selection or switching to one of the remaining closed doors uniformly at random? How should you play? Justify your answer with rigorous
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