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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":"c21ac66c-fc12-42af-a2e9-b29dc615a9e1"},{"params":{"media":{"type":{"params":{"contentName":"Bild","file":{"path":"images\/file-5e9838a903fca.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":1920,"height":1079},"alt":"Catan"},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"U","title":"Unbenannt: Image","defaultLanguage":"de"},"subContentId":"7b58e39c-b4a0-454a-bb08-4fa173c6c845"},"disableImageZooming":false},"text":"

Beim Spiel \"Die Siedler von Catan\" wirft man gleichzeitig mit zwei W\u00fcrfeln und betrachtet die Augensumme beider W\u00fcrfel.
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a) Die *Zufallsgr\u00f6\u00dfe\/Zufallsvariable* X gibt die Augensumme beider W\u00fcrfel an.<\/p>\n\n

b) X kann insgesamt *11* verschiedene Werte annehmen.<\/p>\n\n

c) p(X = 2) = *1*\/36 p(X = 11) = *2*\/36 p(X = 7) = *6*\/36<\/p>\n\n

d) p(X > 2) = 1 - p(X *=* 2)<\/p>\n\n

e) Summiert man alle Wahrscheinlichkeiten von X, so erh\u00e4lt man den Wert *1*.<\/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":"CC0 1.0","title":"Catan","authors":[{"name":"heidenreich","role":"Author"}],"source":"https:\/\/pixabay.com\/de\/photos\/catan-brettspiel-wettbewerb-4494043\/","defaultLanguage":"de"},"subContentId":"a7252b18-e6d8-467f-9780-23f29f42cc46"},{"params":{"media":{"disableImageZooming":false},"text":"

Bestimme jeweils den Erwartungswert E(X) der Zufallsgr\u00f6\u00dfe X.<\/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) X = \"Augenzahl beim Werfen eines Spielw\u00fcrfels\"<\/p>\n\n

E(X) = *3,5\/3.5*<\/p>\n\n

b) X = \"Augensumme beim Werfen zweier Spielw\u00fcrfels\"<\/p>\n\n

E(X) = *7*<\/p>\n\n

c) Man darf f\u00fcr einen Spieleinsatz von 20 Cent einmal w\u00fcrfeln. Als Auszahlung erh\u00e4lt man die Quadratzahl der Augenzahl in Cent ausbezahlt.<\/p>\n\n

X = \"Gewinn in Cent\"<\/p>\n\n

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Entweder A oder B<\/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 Mengendiagramme der logischen Aussage zu.","defaultLanguage":"de"},"subContentId":"96919ed4-fbc4-4028-ad58-d8d48f788ee7"},{"params":{"media":{"type":{"params":{"contentName":"Bild","file":{"path":"images\/file-5e9f019fe297f.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":1920,"height":1436}},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"CC0 1.0","title":"Unbenannt: Image","authors":[{"name":"heidenreich","role":"Author"}],"source":"https:\/\/pixabay.com\/de\/photos\/w%C3%BCrfel-sechs-gl%C3%BCcksspiel-spielen-689618\/","defaultLanguage":"de"},"subContentId":"2fed9c22-a0bc-4527-8bd6-224f1d3cac19"},"disableImageZooming":false},"text":"

Ein W\u00fcrfel wird zweimal geworfen.
\nBestimme jeweils die Wahrscheinlichkeit (runde auf zwei Stellen hinter dem Komma).<\/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":true,"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) A: \"Der erste Wurf zeigt eine 1, wenn die Augensumme h\u00f6chstens 4 betr\u00e4gt.\"<\/p>\n\n

P(A) = *0,5\/0.5\/0,50\/0.50\/50%*<\/p>\n\n

b) B: \"Die Augensumme betr\u00e4gt mindestens 8, wenn der erste Wurf eine 5 ist.\"<\/p>\n\n

P(B) = * 0,67\/0.67\/67%*<\/p>\n\n

c) C: \"Die Augensumme ist gerade, wenn die Augensumme gr\u00f6\u00dfer 8 ist.\"<\/p>\n\n

P(C) = *0,4\/0.4\/0,40\/0.40\/40%*<\/p>\n\n

d) D: \"Die Augensumme ungerade ist, wenn die Augensumme 5 ist.\"<\/p>\n\n

P(D) = *1\/1,00\/1.00\/100%*<\/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":"W\u00fcrfelwurf","defaultLanguage":"de"},"subContentId":"de63ce5d-48a0-422a-9b9b-f49e55e1016a"},{"params":{"media":{"disableImageZooming":false,"type":{"params":{"contentName":"Bild","file":{"path":"images\/file-5e9f007a4be24.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":655,"height":202}},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"U","title":"Unbenannt: Image","defaultLanguage":"de"},"subContentId":"795b7e11-ea97-4ecf-9420-074f2a255570"}},"text":"

Die abgebildete Vierfeldertafel zeigt, wie viele der Sch\u00fclerinnen und Sch\u00fcler des LBS-Gymnasiums in der Mittelstufe sind (M) und wie viele mit dem Fahrrad in die Schule fahren (F).<\/p>\n\n

Bestimme hierzu folgende Wahrscheinlichkeiten.<\/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) Mit welcher Wahrscheinlichkeit ist ein Sch\u00fcler in der Mittelstufe?<\/p>\n\n

\\( P(M) \\) = *0,32\/0.32\/32%*<\/p>\n\n

b) Mit welcher Wahrscheinlichkeit kommt ein Sch\u00fcler mit dem Fahrrad in die Schule?<\/p>\n\n

\\( P(F) \\) = *0,22\/0.22\/22%*<\/p>\n\n

c) Mit welcher Wahrscheinlichkeit kommt ein Sch\u00fcler, der aus der Mittelstufe ist, mit dem Fahrrad in
\n die Schule?<\/p>\n\n

\\( P_{M}(F) \\) = *0,4375\/0.4375\/0,44\/0.44\/44%*<\/p>\n\n

d) Mit welcher Wahrscheinlichkeit ist ein zuf\u00e4llig ausgew\u00e4hlter Sch\u00fcler ein Sch\u00fcler aus der
\n Mittelstufe, der mit dem Fahrrad in die Schule kommt?<\/p>\n\n

\\( P(M \u2229 F) \\) = *0,14\/0.14\/14%*<\/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":"Vierfeldertafel","defaultLanguage":"de"},"subContentId":"684a7f45-de07-4e64-ad41-f10bed96d249"},{"params":{"media":{"disableImageZooming":false,"type":{"params":{"contentName":"Bild","file":{"path":"images\/file-5ea0237252297.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":644,"height":205}},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"U","title":"Unbenannt: Image","defaultLanguage":"de"},"subContentId":"598de90b-674b-4772-b2af-dee3fe3cdfbe"}},"text":"

Die abgebildete Vierfeldertafel zeigt, wie viele M\u00e4dchen und Jungen der 7-ten Klasse des LBS-Gymnasiums einen sprachlichen Zweig oder keinen sprachlichen Zweig gew\u00e4hlt haben.<\/p>\n\n

Beantworte hierzu folgende Fragen (runde auf zwei Stellen hinter dem Komma).<\/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) Mit welcher Wahrscheinlichkeit ist ein zuf\u00e4lliger Sch\u00fcler der 7-ten Klasse ein M\u00e4dchen?<\/p>\n\n

\\( P(M) \\) = *0,57\/0.57\/57%*<\/p>\n\n

b) Mit welcher Wahrscheinlichkeit w\u00e4hlt ein zuf\u00e4lliger Sch\u00fcler der 7-ten Klasse den sprachlichen Zweig?<\/p>\n\n

\\( P(S) \\) = *0,40\/0.40\/0,4\/0.4\/40%*<\/p>\n\n

c) Mit welcher Wahrscheinlichkeit w\u00e4hlt ein M\u00e4dchen der 7-ten Klasse den sprachlichen Zweig?<\/p>\n\n

\\( P_{M}(S) \\) = *0,40\/0.40\/0,4\/0.4\/40%*<\/p>\n\n

d) Was folgt aus den Ergebnissen von b) und c) ?<\/p>\n\n

Die beiden Ereignisse \"M\" und \"S\" sind stochastisch *unabh\u00e4ngig* .<\/p>\n\n

<\/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":"Stochastische Unabh\u00e4ngigkeit","defaultLanguage":"de"},"subContentId":"930b209e-d880-451a-b0dc-c8402df35fc7"}]}

Wahrscheinlichkeit: Erwartungswert, Pfadregel, Baumdiagramm