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- Monty_Hall_problem abstract "The Monty Hall problem is a brain teaser, in the form of a probability puzzle (Gruber, Krauss and others), loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975 (Selvin 1975a), (Selvin 1975b). It became famous as a question from a reader's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990 (vos Savant 1990a):Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?Vos Savant's response was that the contestant should switch to the other door. (vos Savant 1990a)The argument relies on assumptions, explicit in extended solution descriptions given by Selvin (1975b) and by vos Savant (1991a), that the host always opens a different door from the door chosen by the player and always reveals a goat by this action—because he knows where the car is hidden. Leonard Mlodinow stated: "The Monty Hall problem is hard to grasp, because unless you think about it carefully, the role of the host goes unappreciated." (Mlodinow 2008)Contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their choice have only a 1/3 chance. One way to see this is to notice that 2/3 of the time, the initial choice of the player is a door hiding a goat. When that is the case, the host is forced to open the other goat door, and the remaining closed door hides the car. "Switching" only fails to give the car when the player picks the "right" door (the door hiding the car) to begin with, which only happens 1/3 of the time.Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong (Tierney 1991). Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy (vos Savant 1991a). Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation confirming the predicted result (Vazsonyi 1999).The Monty Hall problem has attracted academic interest from the surprising result and simple formulation. Variations of the Monty Hall problem are made by changing the implied assumptions and can create drastically different consequences. For one variation, if Monty only offers the contestant a chance to switch when the contestant initially chose the door hiding the car, then the contestant should never switch. For another variation, if Monty opens another door randomly and happens to reveal a goat, then it makes no difference (Rosenthal, 2005a), (Rosenthal, 2005b).The problem is a paradox of the veridical type, because the correct result (you should switch doors) is so counterintuitive it can seem absurd, but is nevertheless demonstrably true. The Monty Hall problem is mathematically closely related to the earlier Three Prisoners problem and to the much older Bertrand's box paradox.".
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- Monty_Hall_problem caption "Null for the door opened, but 2/3 for the host's second still unopened door.".
- Monty_Hall_problem caption "Player's pick has a 1/3 chance on the car and 2/3 chance on a goat. As each one has 1/3 chance on the car, the combined chance of door 2 and door 3 hiding the car is 2/3.".
- Monty_Hall_problem caption "With the usual assumptions, after the host deliberately opened a door to intentionally show a goat, but without any further information, the player's pick still retains its 1/3 chance, likewise the other two doors still retain their combined 2/3 chance:".
- Monty_Hall_problem direction "vertical".
- Monty_Hall_problem hasPhotoCollection Monty_Hall_problem.
- Monty_Hall_problem image "Monty closed doors.svg".
- Monty_Hall_problem image "Monty open door chances.svg".
- Monty_Hall_problem quote ""You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I'll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don't need the world's highest IQ propagating more. Shame!" - Scott Smith, Ph.D. University of Florida".
- Monty_Hall_problem width "176".
- Monty_Hall_problem width "197".
- Monty_Hall_problem width "220".
- Monty_Hall_problem subject Category:Decision_theory_paradoxes.
- Monty_Hall_problem subject Category:Game_theory.
- Monty_Hall_problem subject Category:Let's_Make_a_Deal.
- Monty_Hall_problem subject Category:Mathematical_problems.
- Monty_Hall_problem subject Category:Microeconomics.
- Monty_Hall_problem subject Category:Named_probability_problems.
- Monty_Hall_problem subject Category:Probability_theory_paradoxes.
- Monty_Hall_problem type Abstraction100002137.
- Monty_Hall_problem type Attribute100024264.
- Monty_Hall_problem type Communication100033020.
- Monty_Hall_problem type Condition113920835.
- Monty_Hall_problem type Contradiction107206887.
- Monty_Hall_problem type DecisionTheoryParadoxes.
- Monty_Hall_problem type Difficulty114408086.
- Monty_Hall_problem type Falsehood106756407.
- Monty_Hall_problem type MathematicalProblems.
- Monty_Hall_problem type Message106598915.
- Monty_Hall_problem type NamedProbabilityProblems.
- Monty_Hall_problem type Paradox106724559.
- Monty_Hall_problem type ProbabilityTheoryParadoxes.
- Monty_Hall_problem type Problem114410605.
- Monty_Hall_problem type State100024720.
- Monty_Hall_problem type Statement106722453.
- Monty_Hall_problem comment "The Monty Hall problem is a brain teaser, in the form of a probability puzzle (Gruber, Krauss and others), loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975 (Selvin 1975a), (Selvin 1975b).".
- Monty_Hall_problem label "Driedeurenprobleem".
- Monty_Hall_problem label "Monty Hall problem".
- Monty_Hall_problem label "Paradoks Monty Halla".
- Monty_Hall_problem label "Problema de Monty Hall".
- Monty_Hall_problem label "Problema de Monty Hall".
- Monty_Hall_problem label "Problema di Monty Hall".
- Monty_Hall_problem label "Problème de Monty Hall".
- Monty_Hall_problem label "Ziegenproblem".
- Monty_Hall_problem label "Парадокс Монти Холла".
- Monty_Hall_problem label "مسألة مونتي هول".
- Monty_Hall_problem label "モンティ・ホール問題".
- Monty_Hall_problem label "蒙提霍爾問題".
- Monty_Hall_problem sameAs Monty_Hallův_problém.
- Monty_Hall_problem sameAs Ziegenproblem.