Document (#43942)

Author
Bischoff, M.
Title
¬Das Dornröschen-Problem spaltet die Mathewelt : Die fabelhafte Welt der Mathematik
Issue
[07.04.2023].
Source
https://www.spektrum.de/kolumne/welche-wahrscheinlichkeit-hat-der-muenzwurf-beim-dornroeschen-problem/2125275?utm_source=pocket-newtab-global-de-DE
Year
2023
Series
Mathematik
Abstract
Seit mehr als 20 Jahren streiten sich Fachleute über den Ausgang eines Gedankenexperiments: Lautet die Antwort ½ oder ?? Beide Seiten haben überzeugende Argumente. Welchem Lager gehören Sie an?
Content
"Das Problem, das die Gemüter der Fachwelt erhitzt, lautet folgendermaßen: Dornröschen erklärt sich bereit, an einem Experiment teilzunehmen, bei dem sie sonntags in Schlaf versetzt wird. Ein Experimentator wirft dann eine Münze. Bei »Kopf« weckt er Dornröschen am Montag auf und verabreicht ihr dann wieder ein Schlafmittel und lässt sie bis Mittwoch schlafen. Falls »Zahl« herauskommt, weckt er Dornröschen ebenfalls am Montag, versetzt sie dann wieder in einen Schlaf und weckt sie am Dienstag wieder, um sie dann nochmals bis Mittwoch zu narkotisieren. Der einzige Unterschied ist also, dass sie bei »Zahl« zweimal und bei »Kopf« einmal geweckt wird. Wichtig dabei ist: Durch das Schlafmittel hat Dornröschen keine Erinnerung daran, ob sie zuvor schon einmal geweckt wurde. Sie kann also nicht unterscheiden, ob Montag oder (falls Zahl fiel) Dienstag ist. Beim Aufwecken verrät der Experimentator Dornröschen nichts: weder den Ausgang des Münzwurfs noch den Tag. Er stellt ihr nach jedem Aufwachen aber eine Frage: Wie hoch ist die Wahrscheinlichkeit, dass die Münze »Kopf« gezeigt hat?"
Field
Mathematik
Object
Dornröschen-Problem

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