Monty Hall Dilemma (W3)
The "Monty Hall Dilemma", "Monty Hall problem" is named for its similarity to the "Let's Make a Deal" television game show hosted by "Monty Hall".Und worin besteht das "Monty Hall Dilemma"?
Der Kandidat kann von drei Türen eine auswählen. Hinter einer Tür befindet sich ein Auto. Hinter den anderen Türen befindet sich jeweils eine Ziege.
Nun öffnet der Moderator eine der nicht gewählten Türen - natürlich eine hinter der sich eine Ziege befindet.
Nun hat der Kandidat die Möglichkeit, seine ursprüngliche Wahl (der Tür) noch einmal zu ändern.
Die Frage ist: Sollte der Kandidat bei seiner ursprüngliche Wahl bleiben oder sollte er die andere (geschlossene) Tür wählen.
Das Ergebnis sei verraten: Die Änderung der Wahl erhöht die Gewinnwahrscheinlichkeit von 1/3 auf 2/3. - Im ersten Moment schwer zu verstehen, aber die Wahrscheinlichkeitsrechnung läßt keinen anderen Schluß zu.
Direkt zu sehen ist, dass die Trefferwahrscheinlichkeit im ersten Durchgang genau 1/3 ist. (Hinter einer von drei Türen befindet sich der Hauptgewinn.)
D.h. heißt aber umgekehrt, dass sich der Hauptgewinn hinter einer der beiden anderen Türen befindet, ist genau 2/3.
Und im zweiten Schritt besteht nun die Möglichkeit von der 1/3-Wahrscheinlichkeit zur 2/3-Wahrscheinlichkeit zu wechseln. Und da dort ja schon eine "Ziegen-Tür" geöffnet wurde, ist die Wahrscheinlichkeit, dass die zweite ungeöffnete Tür die "Auto-Tür" ist gleich 2/3.
Bei 99 Durchläufen der gleichen Testsituation würde der Kandidat also etwa 66 Autos gewinnen und etwa 33 Ziegen.
(E?)(L?) http://www.cut-the-knot.org/hall.shtml
The "Monty Hall Dilemma" was discussed in the popular "Ask Marylin" question-and-answer column of the Parade magazine. Details can also be found in the "Power of Logical Thinking" by Marylin vos Savant, St. Martin's Press, 1996.
Marylin received the following question:
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 number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors?
Craig. F. Whitaker, Columbia, MD
Marylin's response caused an avalanche of correspondence, mostly from people who would not accept her solution. Several iterations of correspondence ensued. Eventually, she issued a call to Math teachers among her readers to organize experiments and send her the charts. Some readers with access to computers ran computer simulations. Years ago I concluded this paragraph with the sentence, At long last, the truth was established and accepted.
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(E?)(L?) https://en.wikipedia.org/wiki/Monty_Hall_problem
The "Monty Hall problem" is a brain teaser, in the form of a probability puzzle, 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 (and solved) in a letter by Steve Selvin to the "American Statistician" in 1975. It became famous as a question from reader Craig F. Whitaker's letter quoted in "Marilyn vos Savant's" "Ask Marilyn" column in Parade magazine in 1990:
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?
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(E?)(L?) https://mathworld.wolfram.com/MontyHallProblem.html
The problem is stated as follows. Assume that a room is equipped with three doors. Behind two are goats, and behind the third is a shiny new car. You are asked to pick a door, and will win whatever is behind it. Let's say you pick door 1. Before the door is opened, however, someone who knows what's behind the doors (Monty Hall) opens one of the other two doors, revealing a goat, and asks you if you wish to change your selection to the third door (i.e., the door which neither you picked nor he opened). The "Monty Hall problem" is deciding whether you do.
The correct answer is that you do want to switch.
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(E1)(L1) http://books.google.com/ngrams/graph?corpus=0&content=Monty Hall Dilemma
Abfrage im Google-Corpus mit 15Mio. eingescannter Bücher von 1500 bis heute.
Engl. "Monty Hall Dilemma" taucht in der Literatur nicht signifikant auf.
Erstellt: 2023-11