\mnb150<nb wrap="0" txtwidth="75" autowidth="0" pprint="1" typeset="1" xface="Times New Roman" xsize="280" xbold="0" xitalic="0" xcolor="#0000FF" slidents="1" sizemult="71" minsize="160" ifont="0 280 255 0 49 Courier New" ofont="0 280 16711680 0 49 Courier New" tfont="0 280 0 0 18 Times New Roman"><cmd><![CDATA[Gluecksrad:= proc(Feld)
  local i, Felder;
begin
  Felder:= [RGB::Green, RGB::Grey, RGB::Red, RGB::Black, RGB::Blue];
  Farben:= [Felder[i] $ i = Feld..5, Felder[i] $ i = 1..Feld-1];
  return( plot( plot::piechart2d([20, 20, 20, 20, 20],
                           Colors = Farben,
                           Moves = [1 = 2] )
         ) );
end_proc:

zufall:= random(1..5):

Drehen:= proc() begin Gluecksrad(zufall()) end_proc:]]></cmd></nb>ÿ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\fswiss\fprq2 Arial;}{\f4\fswiss\fprq2 Helvetica;}{\f5\fmodern\fprq1 Courier New;}}
{\colortbl\red0\green0\blue0;\red255\green0\blue0;\red128\green0\blue0;\red0\green128\blue0;\red255\green255\blue255;\red0\green0\blue255;\red128\green128\blue128;\red0\green255\blue0;}
\deflang1031\pard\ri4\plain\f5\fs20\cf0\b ________________________________________________________________________________
\par 
\par Inhalt....: Einf\'fchrung in die Wahrscheinlichkeitsrechnung
\par Kategorie.: Unterrichtsmaterial
\par Mathematik: Stochastik
\par MuPAD.....: 3.0.0
\par Datum.....: 2003-03-04
\par Autoren...: Kai Gehrs <acrowley@mupad.de>
\par Funktionen: expand, plot::Piechart3d, Moves, Colors
\par ________________________________________________________________________________
\par \plain\f3\fs28\cf0 
\par \plain\f3\fs36\cf0\b Einf\'fchrung in die Wahrscheinlichkeitsrechnung am
\par Beispiel eines Gl\'fccksrad-Spiels
\par \plain\f3\fs28\cf0 
\par \plain\f3\fs24\cf3 Dieses Notebook erm\'f6glicht eine interaktive Einf\'fchrung in die Wahrscheinlichkeitsrechnung
\par mit Hilfe eines Computeralgebrasystems. Am Beispiel eines Gl\'fccksrads k\'f6nnen die
\par Sch\'fclerInnen experimentell den Zusammenhang zwischen relativer H\'e4ufigkeit und der
\par Wahrscheinlichtkeit eines Ereignisses erfahren. Ferner bietet sich die M\'f6glichkeit
\par Rechenregeln f\'fcr die Wahrscheinlichkeit \'fcber das Experiment zu motivieren oder den
\par Erwartungswert binomialverteilter Zufallsgr\'f6\'dfen dar\'fcber einzuf\'fchren.
\par \plain\f3\fs24\cf0 
\par 
\par \plain\f3\fs24\cf2\b Motivation und Konzept des Arbeitsblatts
\par \plain\f3\fs24\cf2 
\par In aktuellen Schulb\'fcchern, die im Mathematikunterricht der Sekundarstufe II eingesetzt werden,
\par wird in der Regel zu Beginn des Abschnitts \'fcber Wahrscheinlichkeitsrechnung der Zusammen-
\par hang zwischen relativer H\'e4ufigkeit und Wahrscheinlichkeit von Ereignissen diskutiert.
\par 
\par H\'e4ufig wird der Satz
\par 
\par \pard\li500\ri4\plain\f3\fs24\cf2\i Mit zunehmender Versuchsanzahl in einem Laplace-Experiment geht die
\par relative H\'e4ufigkeit eines Ereignisses in seine Wahrscheinlichkeit \'fcber.
\par \plain\f3\fs24\cf2 
\par \pard\ri4\plain\f3\fs24\cf2 von Sch\'fclerInnen (zu Recht) mit Skepsis aufgenommen. Die Aussage scheint nicht verifizierbar
\par und im Unterricht (auch im Rahmen eines Mathematik-Leistungskurses) kann keinesfalls die
\par n\'f6tige Theorie entwickelt werden, um diesen Sachverhalt mathematisch korrekt verifizieren
\par zu k\'f6nnen. Einen Ausweg bietet ein experimenteller Zugang wie er z.B. im Rahmen dieses
\par Notebooks erm\'f6glicht wird.
\par 
\par 
\par \plain\f3\fs24\cf2\b Unterrichtliche Voraussetzungen
\par \plain\f3\fs24\cf2 
\par Dieses Notebook setzt keinerlei besondere Kenntnisse rund um MuPAD voraus. Die hier
\par vorgestellten Prozeduren m\'fcssen keinesfalls von den Sch\'fclerInnen nachvollzogen werden.
\par Sie sind lediglich als "n\'fctzliche Werkzeuge" zu bezeichnen - \'e4hnlich dem, als wenn man
\par die Sch\'fclerInnen mit W\'fcrfeln ausr\'fcstet und sie auf diesem Weg Wahrscheinlichkeits-
\par experimente praktisch durchf\'fchren l\'e4sst. Die mathematischen Voraussetzungen sind
\par ebenfalls sehr gering. Nach einer kurzen Erl\'e4uterung des Begriffs der relativen H\'e4ufigkeit
\par kann mit diesem Notebook noch vor der Einf\'fchrung der Wahrscheinlichkeit experimentiert
\par werden. Weiter unten finden sich auch Anregungen, wie sich die hier vorgestellten Proze-
\par duren auch im Kontext der Vermittlung von Rechenregeln f\'fcr Laplace-Wahrscheinlichkeiten
\par oder im Kontext von Erwartungswerten binomialverteilter Zufallsgr\'f6\'dfen eignen. Zu diesem
\par Zweck sind dann entsprechende Vorbereitungen mathematischer Natur aus dem Unterricht,
\par wie z.B. Einf\'fchrung der Binomialverteilung etc., n\'f6tig.
\par \plain\f3\fs28\cf0 
\par Nachdem die relative H\'e4ufigkeit im Unterricht eingef\'fchrt wurde, erhalten
\par die Sch\'fclerInnen die Aufgabe, "Gl\'fccksrad" zu spielen:
\par 
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