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Die Wahrscheinlichkeit f\u00fcr die Farbe *gelb\/Gelb* ist am gr\u00f6\u00dften. Sie betr\u00e4gt *50*%.<\/p>\n\n

Die Wahrscheinlichkeiten f\u00fcr die Farbe Blau und die Farbe Gr\u00fcn sind *gleich* gro\u00df. Sie betr\u00e4gt jeweils *12,5\/12.5*%.<\/p>\n\n

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Das Blatt im Skat besteht aus 32 Karten, jeweils 8 Karten Pik, Kreuz, Karo und Herz. Die Symbole sind sieben, acht, neun, zehn, Bube, Dame, K\u00f6nig und Ass.<\/p>\n\n

Es wird nun eine Karte gezogen. Trage f\u00fcr die folgenden Ereignisse die Wahrscheinlichkeit ein.<\/p>\n\n

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P (\"rote Karte\") = *16* \/ 32<\/p>\n\n

P (\"Herz-Karte\") = *8* \/ 32<\/p>\n\n

P (\"Herz-Dame\") = *1* \/ 32<\/p>\n\n

P (\"Ass\") = *4* \/ 32<\/p>\n\n

P (\"roter Bube\") = *2* \/ 32<\/p>\n\n

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Trage die fehlenden Werte ein.<\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":false,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["

Ein W\u00fcrfel wird zweimal geworfen.<\/p>\n\n

Bestimme die Wahrscheinlichkeiten.<\/p>\n\n

<\/p>\n\n

P ((6 ; 6)) = *1* \/ 36<\/p>\n\n

P ((3 ; 3)) = *1* \/ 36<\/p>\n\n

P ((4 ; 6)) = *1* \/ 36<\/p>\n\n

P (\"gerade Zahl ; gerade Zahl\") = *9* \/ 36<\/p>\n\n

P (\"6 im ersten Wurf\" und \"keine 6 im zweiten Wurf\") = *5* \/ 36<\/p>\n\n

P (\"mindestens eine 6\") = *11* \/ 36<\/p>\n\n

P (\"h\u00f6chstens eine 6\") = *35* \/ 36<\/p>\n\n

P (\"genau eine 6\") = *10* \/ 36<\/p>\n"],"a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Eingaben werden als richtig, falsch oder unbeantwortet markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Eingaben werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet.","a11yCheckingModeHeader":"\u00dcberpr\u00fcfen-Modus aktiv"},"library":"H5P.Blanks 1.12","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Mehrstufiges Zufallexperiment","defaultLanguage":"de"},"subContentId":"f7b57a8a-d6ff-45c0-b318-654f3794d4c6"},{"params":{"media":{"type":{"params":{"contentName":"Bild","file":{"path":"images\/file-5df20aee8b0d1.png","mime":"image\/png","copyright":{"license":"U"},"width":1175,"height":1280},"alt":"Lotteriemaschine"},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"U","title":"Unbenannt: Image","defaultLanguage":"de"},"subContentId":"05189eb1-af82-41f7-887a-c07f89a66ea4"},"disableImageZooming":false},"text":"

Lotto 6 aus 49 ist ein sehr beliebtes Gl\u00fccksspiel. Berechne die Wahrscheinlichkeit f\u00fcr 6 Richtige. Trage die fehlenden W\u00f6rter in den Text ein.<\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":false,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["

Beim Lotto 6 aus 49 gibt es insgesamt *49* verschiedene Kugeln.<\/p>\n\n

Wir betrachten die Wahrscheinlichkeit f\u00fcr sechs richtige Zahlen, die du zuvor getippt hast.<\/p>\n\n

Die Wahrscheinlichkeit, dass dein Tipp die erste gezogene Kugel enth\u00e4lt, ist *6* zu 49.<\/p>\n\n

In der Lotterie-Maschine sind danach nur noch *48* Kugeln.<\/p>\n\n

Die Wahrscheinlichkeit, dass dein Tipp auch die zweite gezogene Kugel enth\u00e4lt, ist jetzt *5* zu 48.<\/p>\n\n

Es handelt sich hierbei um ein *mehrstufiges\/Mehrstufiges* Zufallsexperiment.<\/p>\n\n

Deshalb musst du die Wahrscheinlichkeiten gem\u00e4\u00df der Pfad-Regel miteinander *multiplizieren*.<\/p>\n\n

Fahre nun f\u00fcr die dritte bis sechste Kugel auf gleiche Weise fort.<\/p>\n\n

Zuletzt musst du insgesamt *6* Br\u00fcche miteinander multiplizieren.<\/p>\n\n

Alle Z\u00e4hler miteinander multipliziert ergeben *720*.<\/p>\n\n

Alle Nenner miteinander multipliziert ergeben *10068347520*. Die Wahrscheinlichkeit ist somit 1 zu *13983816*.<\/p>\n\n

Selbst wenn du jeden Tag Lotto spielen w\u00fcrdest, m\u00fcsstest du etwa *38312* Jahre warten um durchschnittlich einmal diesen Gewinn zu erzielen.<\/p>\n\n

Ich w\u00fcrde mir deshalb dies nochmals \u00fcberlegen ;-)<\/p>\n"],"a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Eingaben werden als richtig, falsch oder unbeantwortet markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Eingaben werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet.","a11yCheckingModeHeader":"\u00dcberpr\u00fcfen-Modus aktiv"},"library":"H5P.Blanks 1.12","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Totto Lotto","defaultLanguage":"de"},"subContentId":"1bab2ef4-3cd2-4a33-9b25-ae210784090d"},{"params":{"scoreShow":"\u00dcberpr\u00fcfen","tryAgain":"Wiederholen","scoreExplanation":"Richtige Antworten geben +1 Punkte. Bei falschen Antworten gibt es -1 Punkt. Die kleinstm\u00f6gliche Punktzahl ist 0.","question":{"settings":{"size":{"width":620,"height":310}},"task":{"elements":[{"x":59.055118110236,"y":59.055118110236,"width":6.1125333169291,"height":7.1804467027559,"dropZones":["0","1","2","3"],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Man w\u00fcrfelt eine gerade Zahl.<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text","defaultLanguage":"de"},"subContentId":"fcf3c778-316d-46ad-bb42-eb65213ab367"},"backgroundOpacity":100,"multiple":false},{"x":0,"y":0,"width":5,"height":5,"dropZones":[],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Man w\u00fcrfelt eine ungerade Zahl.<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text","defaultLanguage":"de"},"subContentId":"df7ef61a-1f78-4f90-8f04-3f53b1993084"},"backgroundOpacity":100,"multiple":false},{"x":21.653543307087,"y":0,"width":5,"height":5,"dropZones":[],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Man w\u00fcrfelt eine zwei oder eine gr\u00f6\u00dfere Zahl.<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text","defaultLanguage":"de"},"subContentId":"89a71b31-f875-4463-a768-4fad00f38367"},"backgroundOpacity":100,"multiple":false},{"x":81.034482758621,"y":58.620689655172,"width":6.6464900098425,"height":7.0825552631528,"dropZones":["0","1","2","3"],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Man w\u00fcrfelt eine eins.<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text","defaultLanguage":"de"},"subContentId":"ddcf74a6-49f5-4f27-b5ff-a87fa0b833a4"},"backgroundOpacity":100,"multiple":false},{"x":37.931034482759,"y":60.344827586207,"width":6.4939309547244,"height":6.9516081200787,"dropZones":["0","1","2","3"],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Man w\u00fcrfelt eine Zahl gr\u00f6\u00dfer als vier.<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text","defaultLanguage":"de"},"subContentId":"5b468b74-9ddd-4c1f-a593-d7d432b8aad5"},"backgroundOpacity":100,"multiple":false},{"x":41.338582677165,"y":0,"width":6.2511147727273,"height":4.9905296122995,"dropZones":[],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Man w\u00fcrfelt eine drei oder eine Zahl kleiner als drei.<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text","defaultLanguage":"de"},"subContentId":"a4dbe8bc-da43-42b3-a987-d7f322d4e687"},"backgroundOpacity":100,"multiple":false},{"x":14.117647058824,"y":60.093896713615,"width":6.4939309547244,"height":6.9516081200787,"dropZones":["0","1","2","3"],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Man w\u00fcrfelt eine Quadratzahl.<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text","defaultLanguage":"de"},"subContentId":"3644aee8-4e21-43cd-9975-273151805400"},"backgroundOpacity":100,"multiple":false},{"x":63.793103448276,"y":0,"width":6.2511147727273,"height":4.9905296122995,"dropZones":[],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Man w\u00fcrfelt eine Zahl gr\u00f6\u00dfer als eins mit Ausnahme der vier.<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text","defaultLanguage":"de"},"subContentId":"e15b349a-ed06-4ff5-8b37-96853dd70b07"},"backgroundOpacity":100,"multiple":false}],"dropZones":[{"x":0,"y":0,"width":6.1023622047244,"height":6.865157480315,"correctElements":["0"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

Ablage f\u00fcr gerade Zahl<\/div>\n"},{"x":19.685039370079,"y":0,"width":6.7888779527559,"height":7.6279527559055,"correctElements":["3"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

ablage Zahl gr\u00f6\u00dfer als 4<\/div>\n"},{"x":63.793103448276,"y":0,"width":7.2465551181102,"height":7.6279527559055,"correctElements":["6"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

Ablageletzte<\/div>\n"},{"x":41.338582677165,"y":0,"width":7.2526737967914,"height":7.2526737967914,"correctElements":["4"],"showLabel":false,"backgroundOpacity":0,"tipsAndFeedback":{"tip":""},"single":true,"autoAlign":true,"label":"

Ablageletzte<\/div>\n"}]}},"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":false,"enableCheckButton":true,"showSolutionsRequiresInput":true,"singlePoint":false,"applyPenalties":true,"enableScoreExplanation":true,"dropZoneHighlighting":"dragging","autoAlignSpacing":2,"enableFullScreen":false,"showScorePoints":true,"showTitle":true},"grabbablePrefix":"Ziehbares Element {num} von {total}.","grabbableSuffix":"Abgelegt in Ablagezone {num}.","dropzonePrefix":"Ablagezone {num} von {total}.","noDropzone":"Keine Ablagezone.","tipLabel":"Hinweis zeigen","tipAvailable":"Hinweis verf\u00fcgbar","correctAnswer":"Richtige Antwort","wrongAnswer":"Falsche Antwort","feedbackHeader":"R\u00fcckmeldung","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","scoreExplanationButtonLabel":"Zeige Erkl\u00e4rung der Punktevergabe","localize":{"fullscreen":"Vollbild","exitFullscreen":"Vollbild beenden"},"a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Eingaben werden als richtig, falsch oder unbeantwortet markiert.","a11yRetry":"Die Aufgabe wiederholen. Alle Versuche werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet."},"library":"H5P.DragQuestion 1.13","metadata":{"contentType":"Drag and Drop","license":"U","title":"Ordne die Ereignisse den Gegenereignissen zu.","defaultLanguage":"de"},"subContentId":"7b650e68-3641-44e9-a244-0bfde8c623c4"},{"params":{"media":{"disableImageZooming":false,"type":{"params":{"contentName":"Bild","file":{"path":"images\/file-5e1dd81a61dd3.png","mime":"image\/png","copyright":{"license":"U"},"width":445,"height":590,"originalImage":{"path":"images\/file-5e1dd80d097d6.png#tmp","mime":"image\/png","height":1193,"width":653}},"alt":"Arztbesuch"},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"U","title":"Unbenannt: Image","defaultLanguage":"de"},"subContentId":"2b5e7c80-3d9d-4848-85ab-14ee64e2a684"}},"answers":[{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"

\u00dcberlege nochmal welche m\u00f6glichen Ergebnisse geh\u00f6ren zum Ereignis h\u00f6chstens 2 Patienten werden geheilt<\/em>? Welche demnach nicht (Gegenereignis)?<\/div>\n","notChosenFeedback":""},"text":"
Kein Patient wird geheilt.<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"
Great answer :-)<\/div>\n","notChosenFeedback":""},"text":"
Alle Patienten werden geheilt.<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"
\u00dcberlege nochmal welche m\u00f6glichen Ergebnisse geh\u00f6ren zum Ereignis h\u00f6chstens 2 Patienten werden geheilt<\/em>? Welche demnach nicht (Gegenereignis)?<\/div>\n","notChosenFeedback":""},"text":"
Mindestens zwei Patienten werden geheilt.<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"
\u00dcberlege nochmal welche m\u00f6glichen Ergebnisse geh\u00f6ren zum Ereignis h\u00f6chstens 2 Patienten werden geheilt<\/em>? Welche demnach nicht (Gegenereignis)?<\/div>\n","notChosenFeedback":""},"text":"
Mindestens ein Patient wird geheilt.<\/div>\n"}],"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":false,"enableSolutionsButton":true,"enableCheckButton":true,"type":"auto","singlePoint":false,"randomAnswers":true,"showSolutionsRequiresInput":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false,"passPercentage":100,"showScorePoints":true},"UI":{"checkAnswerButton":"\u00dcberpr\u00fcfen","showSolutionButton":"L\u00f6sung anzeigen","tryAgainButton":"Wiederholen","tipsLabel":"Hinweis anzeigen","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","tipAvailable":"Hinweis verf\u00fcgbar","feedbackAvailable":"R\u00fcckmeldung verf\u00fcgbar","readFeedback":"R\u00fcckmeldung vorlesen","wrongAnswer":"Falsche Antwort","correctAnswer":"Richtige Antwort","shouldCheck":"H\u00e4tte gew\u00e4hlt werden m\u00fcssen","shouldNotCheck":"H\u00e4tte nicht gew\u00e4hlt werden sollen","noInput":"Bitte antworte, bevor du die L\u00f6sung ansiehst","a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Auswahlen werden als richtig, falsch oder fehlend markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Versuche werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet."},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"
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L\u00f6se die folgenden kombinatorischen Aufgaben indem du die L\u00fccken ausf\u00fcllst.Trage die fehlenden W\u00f6rter ein.<\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":false,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["
a) Ein Fahrradschlo\u00df hat drei Ringe, bei denen man die Ziffern 0 bis 9 einstellen kann.<\/p>\n\n
Es gibt insgesamt *1000* verschiedene Kombinationen.<\/p>\n\n
b) Beim Fu\u00dfballtoto muss man entweder eine 1 (Heimsieg), eine 0 (Unentschieden) oder eine 2 (Ausw\u00e4rtssieg) tippen. Es gibt 5 Spiele.<\/p>\n\n
Es gibt insgesamt *243* verschiedene Tipps.<\/p>\n\n
c) Bei einem Sportwettkampf nehmen 10 Teilnehmer teil. Es gibt eine Goldmedaille (Erster), eine Silbermedaille (Zweiter) und eine Bronzemedaille (dritter).<\/p>\n\n
Es gibt *720* verschiedene M\u00f6glichkeiten f\u00fcr die ersten drei Pl\u00e4tze.<\/p>\n"],"a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Eingaben werden als richtig, falsch oder unbeantwortet markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Eingaben werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet.","a11yCheckingModeHeader":"\u00dcberpr\u00fcfen-Modus aktiv"},"library":"H5P.Blanks 1.12","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Kombinatorik","defaultLanguage":"de"},"subContentId":"7995b197-d11a-46eb-8b02-2f39f9c8a83d"}]}

Wahrscheinlichkeitsrechnung Einführung