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Interactive Laplace Experiment Quiz

Interactive Laplace Experiment Quiz
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2025-01-29 22:43
In collections Laplace-Wahrscheinlichkeit
This GeoGebra example demonstrates Laplace random experiments through interactive multiple-choice and open-ended questions. Core mathematical concepts include: equally likely outcomes, Laplace probability formula (p=1/n), and the relationship between relative frequency and probability. Construction uses GeoGebra commands including Sequence, Element, Random, If for random number generation, conditi

GeoGebra Commands & Parameters

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {8, 3, 2, 4, 3, 5, 6, 3, 6, 9}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  5. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  6. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte, {{(0.049999999999999996, 10.059999999999993), (1.05250626566416, 10.059999999999993), (2.0550125313283196, 10.059999999999993), (3.05751879699248, 10.059999999999993), (4.060025062656639, 10.059999999999993), (5.0625313283208, 10.059999999999993), (6.06503759398496, 10.059999999999993), (7.06754385964912, 10.059999999999993), (8.07005012531328, 10.059999999999993), (9.072556390977441, 10.059999999999993), (10.0750626566416, 10.059999999999993), (11.07756892230576, 10.059999999999993), (12.080075187969921, 10.059999999999993), (13.08258145363408, 10.059999999999993), (14.08508771929824, 10.059999999999993), (15.087593984962401, 10.059999999999993), (16.09010025062656, 10.059999999999993)}, {(0.049999999999999996, 9.056655518394644), (1.05250626566416, 9.056655518394644), (2.0550125313283196, 9.056655518394644), (3.05751879699248, 9.056655518394644), (4.060025062656639, 9.056655518394644), (5.0625313283208, 9.056655518394644), (6.06503759398496, 9.056655518394644), (7.06754385964912, 9.056655518394644), (8.07005012531328, 9.056655518394644), (9.072556390977441, 9.056655518394644), (10.0750626566416, 9.056655518394644), (11.07756892230576, 9.056655518394644), (12.080075187969921, 9.056655518394644), (13.08258145363408, 9.056655518394644), (14.08508771929824, 9.056655518394644), (15.087593984962401, 9.056655518394644), (16.09010025062656, 9.056655518394644)}, {(0.049999999999999996, 8.053311036789292), (1.05250626566416, 8.053311036789292), (2.0550125313283196, 8.053311036789292), (3.05751879699248, 8.053311036789292), (4.060025062656639, 8.053311036789292), (5.0625313283208, 8.053311036789292), (6.06503759398496, 8.053311036789292), (7.06754385964912, 8.053311036789292), (8.07005012531328, 8.053311036789292), (9.072556390977441, 8.053311036789292), (10.0750626566416, 8.053311036789292), (11.07756892230576, 8.053311036789292), (12.080075187969921, 8.053311036789292), (13.08258145363408, 8.053311036789292), (14.08508771929824, 8.053311036789292), (15.087593984962401, 8.053311036789292), (16.09010025062656, 8.053311036789292)}, {(0.049999999999999996, 7.049966555183943), (1.05250626566416, 7.049966555183943), (2.0550125313283196, 7.049966555183943), (3.05751879699248, 7.049966555183943), (4.060025062656639, 7.049966555183943), (5.0625313283208, 7.049966555183943), (6.06503759398496, 7.049966555183943), (7.06754385964912, 7.049966555183943), (8.07005012531328, 7.049966555183943), (9.072556390977441, 7.049966555183943), (10.0750626566416, 7.049966555183943), (11.07756892230576, 7.049966555183943), (12.080075187969921, 7.049966555183943), (13.08258145363408, 7.049966555183943), (14.08508771929824, 7.049966555183943), (15.087593984962401, 7.049966555183943), (16.09010025062656, 7.049966555183943)}, {(0.049999999999999996, 6.046622073578592), (1.05250626566416, 6.046622073578592), (2.0550125313283196, 6.046622073578592), (3.05751879699248, 6.046622073578592), (4.060025062656639, 6.046622073578592), (5.0625313283208, 6.046622073578592), (6.06503759398496, 6.046622073578592), (7.06754385964912, 6.046622073578592), (8.07005012531328, 6.046622073578592), (9.072556390977441, 6.046622073578592), (10.0750626566416, 6.046622073578592), (11.07756892230576, 6.046622073578592), (12.080075187969921, 6.046622073578592), (13.08258145363408, 6.046622073578592), (14.08508771929824, 6.046622073578592), (15.087593984962401, 6.046622073578592), (16.09010025062656, 6.046622073578592)}, {(0.049999999999999996, 5.043277591973242), (1.05250626566416, 5.043277591973242), (2.0550125313283196, 5.043277591973242), (3.05751879699248, 5.043277591973242), (4.060025062656639, 5.043277591973242), (5.0625313283208, 5.043277591973242), (6.06503759398496, 5.043277591973242), (7.06754385964912, 5.043277591973242), (8.07005012531328, 5.043277591973242), (9.072556390977441, 5.043277591973242), (10.0750626566416, 5.043277591973242), (11.07756892230576, 5.043277591973242), (12.080075187969921, 5.043277591973242), (13.08258145363408, 5.043277591973242), (14.08508771929824, 5.043277591973242), (15.087593984962401, 5.043277591973242), (16.09010025062656, 5.043277591973242)}, {(0.049999999999999996, 4.039933110367891), (1.05250626566416, 4.039933110367891), (2.0550125313283196, 4.039933110367891), (3.05751879699248, 4.039933110367891), (4.060025062656639, 4.039933110367891), (5.0625313283208, 4.039933110367891), (6.06503759398496, 4.039933110367891), (7.06754385964912, 4.039933110367891), (8.07005012531328, 4.039933110367891), (9.072556390977441, 4.039933110367891), (10.0750626566416, 4.039933110367891), (11.07756892230576, 4.039933110367891), (12.080075187969921, 4.039933110367891), (13.08258145363408, 4.039933110367891), (14.08508771929824, 4.039933110367891), (15.087593984962401, 4.039933110367891), (16.09010025062656, 4.039933110367891)}, {(0.049999999999999996, 3.0365886287625408), (1.05250626566416, 3.0365886287625408), (2.0550125313283196, 3.0365886287625408), (3.05751879699248, 3.0365886287625408), (4.060025062656639, 3.0365886287625408), (5.0625313283208, 3.0365886287625408), (6.06503759398496, 3.0365886287625408), (7.06754385964912, 3.0365886287625408), (8.07005012531328, 3.0365886287625408), (9.072556390977441, 3.0365886287625408), (10.0750626566416, 3.0365886287625408), (11.07756892230576, 3.0365886287625408), (12.080075187969921, 3.0365886287625408), (13.08258145363408, 3.0365886287625408), (14.08508771929824, 3.0365886287625408), (15.087593984962401, 3.0365886287625408), (16.09010025062656, 3.0365886287625408)}, {(0.049999999999999996, 2.033244147157191), (1.05250626566416, 2.033244147157191), (2.0550125313283196, 2.033244147157191), (3.05751879699248, 2.033244147157191), (4.060025062656639, 2.033244147157191), (5.0625313283208, 2.033244147157191), (6.06503759398496, 2.033244147157191), (7.06754385964912, 2.033244147157191), (8.07005012531328, 2.033244147157191), (9.072556390977441, 2.033244147157191), (10.0750626566416, 2.033244147157191), (11.07756892230576, 2.033244147157191), (12.080075187969921, 2.033244147157191), (13.08258145363408, 2.033244147157191), (14.08508771929824, 2.033244147157191), (15.087593984962401, 2.033244147157191), (16.09010025062656, 2.033244147157191)}, {(0.049999999999999996, 1.0298996655518398), (1.05250626566416, 1.0298996655518398), (2.0550125313283196, 1.0298996655518398), (3.05751879699248, 1.0298996655518398), (4.060025062656639, 1.0298996655518398), (5.0625313283208, 1.0298996655518398), (6.06503759398496, 1.0298996655518398), (7.06754385964912, 1.0298996655518398), (8.07005012531328, 1.0298996655518398), (9.072556390977441, 1.0298996655518398), (10.0750626566416, 1.0298996655518398), (11.07756892230576, 1.0298996655518398), (12.080075187969921, 1.0298996655518398), (13.08258145363408, 1.0298996655518398), (14.08508771929824, 1.0298996655518398), (15.087593984962401, 1.0298996655518398), (16.09010025062656, 1.0298996655518398)}, {(0.049999999999999996, 0.026555183946490146), (1.05250626566416, 0.026555183946490146), (2.0550125313283196, 0.026555183946490146), (3.05751879699248, 0.026555183946490146), (4.060025062656639, 0.026555183946490146), (5.0625313283208, 0.026555183946490146), (6.06503759398496, 0.026555183946490146), (7.06754385964912, 0.026555183946490146), (8.07005012531328, 0.026555183946490146), (9.072556390977441, 0.026555183946490146), (10.0750626566416, 0.026555183946490146), (11.07756892230576, 0.026555183946490146), (12.080075187969921, 0.026555183946490146), (13.08258145363408, 0.026555183946490146), (14.08508771929824, 0.026555183946490146), (15.087593984962401, 0.026555183946490146), (16.09010025062656, 0.026555183946490146)}, {(0.049999999999999996, -0.9767892976588595), (1.05250626566416, -0.9767892976588595), (2.0550125313283196, -0.9767892976588595), (3.05751879699248, -0.9767892976588595), (4.060025062656639, -0.9767892976588595), (5.0625313283208, -0.9767892976588595), (6.06503759398496, -0.9767892976588595), (7.06754385964912, -0.9767892976588595), (8.07005012531328, -0.9767892976588595), (9.072556390977441, -0.9767892976588595), (10.0750626566416, -0.9767892976588595), (11.07756892230576, -0.9767892976588595), (12.080075187969921, -0.9767892976588595), (13.08258145363408, -0.9767892976588595), (14.08508771929824, -0.9767892976588595), (15.087593984962401, -0.9767892976588595), (16.09010025062656, -0.9767892976588595)}, {(0.049999999999999996, -1.9801337792642109), (1.05250626566416, -1.9801337792642109), (2.0550125313283196, -1.9801337792642109), (3.05751879699248, -1.9801337792642109), (4.060025062656639, -1.9801337792642109), (5.0625313283208, -1.9801337792642109), (6.06503759398496, -1.9801337792642109), (7.06754385964912, -1.9801337792642109), (8.07005012531328, -1.9801337792642109), (9.072556390977441, -1.9801337792642109), (10.0750626566416, -1.9801337792642109), (11.07756892230576, -1.9801337792642109), (12.080075187969921, -1.9801337792642109), (13.08258145363408, -1.9801337792642109), (14.08508771929824, -1.9801337792642109), (15.087593984962401, -1.9801337792642109), (16.09010025062656, -1.9801337792642109)}}
  7. Textfield(input031) → InputBox031
  8. Textfield(input061) → InputBox061
  9. Textfield(input062) → InputBox062
  10. PolyLine(PosSB01, Corner[txt011, 1] + (-0.1, 0.5), Corner[txt011, 1] + (-0.1, 0), Corner[txt011, 2] + (0.1, 0), Corner[txt011, 3] + (0.1, 0.1), Corner[txt011, 4] + (-0.1, 0.1), Corner[txt011, 1] + (-0.1, 1.25), PosSB01) → sb01
  11. PolyLine(PosSB03, Corner[txt031, 1] + (0.3, 0), Corner[txt031, 2] + (0.1, 0), Corner[txt031, 3] + (0.1, 0.1), Corner[txt031, 4] + (-0.1, 0.1), Corner[txt031, 1] + (-0.1, 0.3), PosSB03) → sb03
  12. PolyLine(PosSB03, Corner[txt061, 1] + (0.3, 0), Corner[txt061, 2] + (0.1, 0), Corner[txt061, 3] + (0.1, 0.1), Corner[txt061, 4] + (-0.1, 0.1), Corner[txt061, 1] + (-0.1, 0.3), PosSB03) → sb06
  13. PolyLine(PosSB03, Corner[txt081, 1] + (0.3, 0), Corner[txt081, 2] + (0.1, 0), Corner[txt081, 3] + (0.1, 0.1), Corner[txt081, 4] + (-0.1, 0.1), Corner[txt081, 1] + (-0.1, 0.3), PosSB03) → sb08
  14. Random(1, 6) → valueDice
  15. Random(10, 30) → endDice
  16. Sequence(Random[1, 11], m, 1, endDice) → RotateDiceList, {2, 7, 4, 3, 6, 9, 9, 11, 4, 8, 9, 4, 3, 5, 7, 7, 5, 3, 11, 3}
  17. If(animationDice ≟ 0, 0, RotateDiceList(animationDice)) → showDR
  18. If(step ≟ 2, AnzahlWürfe02 ≥ 3 ∧ (animationDice ≟ 0 ∨ animationDice ≟ endDice), true, step ≟ 3, correct031 ∧ option033, step ≟ 5, option051, step ≟ 6, correct061 ∧ correct062, step ≟ 7, correct071 ∧ correct072 ∧ correct073 ∧ correct074 ∧ correct075) → clickableBtnNext
  19. Sequence(PosStartMC03DD + (k * (0, disPixY)), k, 0, 3) → PosMC03
  20. Text("\textsf{Es ist wahrscheinlicher eine 1 als eine 6 zu würfeln.}", Corner[4] + (RasterPixMat * PosMC03(1)) + disMC, false, true, 1, 0) → txtO031
  21. Text("\textsf{Es ist wahrscheinlicher eine gerade Augenzahl als eine\\ungerade Augenzahl zu würfeln.}", Corner[4] + (RasterPixMat * PosMC03(2)) + disMC, false, true, 1, 0) → txtO032
  22. Text("\textsf{Jede Augenzahl kann gleich wahrscheinlich gewürfelt werden.}", Corner[4] + (RasterPixMat * PosMC03(3)) + disMC, false, true, 1, 0) → txtO033
  23. Text("\textsf{Es ist sicher, dass keine 6 gewürfelt wird.}", Corner[4] + (RasterPixMat * PosMC03(4)) + disMC, false, true, 1, 0) → txtO034
  24. Sequence(PosStartMC05DD + (k * (0, disPixY)), k, 0, 1) → PosMC05
  25. Text("\textsf{Laplace-Zufallsexperiment}", Corner[4] + (RasterPixMat * PosMC05(1)) + disMC, false, true, 1, 0) → txtO051
  26. Text("\textsf{kein Laplace-Zufallsexperiment}", Corner[4] + (RasterPixMat * PosMC05(2)) + disMC, false, true, 1, 0) → txtO052
  27. Flatten({PolyLine[PosTable + {(0, 0), ((6 * spalte), 0), ((6 * spalte), (-zeile1) - zeile2 - zeile3), (0, (-zeile1) - zeile2 - zeile3), (0, 0)}], Segment[PosTable + (0, (-zeile1)), PosTable + ((6 * spalte), (-zeile1))], Segment[PosTable + (0, (-zeile1) - zeile2), PosTable + ((6 * spalte), (-zeile1) - zeile2)], Sequence[Segment[PosTable + ((k * spalte), (-zeile1)), PosTable + ((k * spalte), (-zeile1) - zeile2 - zeile3)], k, 1, 5]}) → table
  28. Text("\textsf{\dfrac{\phantom{ }}{\phantom{ }}}", Midpoint[PosTable + ((0 * spalte), (-zeile1) - zeile2), PosTable + ((0 * spalte), (-zeile1) - zeile2 - zeile3)] + (disTable, 0), false, true, 1, 0) → txtF71
  29. Textfield(inputF711) → InputBoxF711
  30. Textfield(inputF712) → InputBoxF712
  31. Text("\textsf{\dfrac{\phantom{ }}{\phantom{ }}}", Midpoint[PosTable + ((1 * spalte), (-zeile1) - zeile2), PosTable + ((1 * spalte), (-zeile1) - zeile2 - zeile3)] + (disTable, 0), false, true, 1, 0) → txtF72
  32. Text("\textsf{\dfrac{\phantom{ }}{\phantom{ }}}", Midpoint[PosTable + ((2 * spalte), (-zeile1) - zeile2), PosTable + ((2 * spalte), (-zeile1) - zeile2 - zeile3)] + (disTable, 0), false, true, 1, 0) → txtF73
  33. Text("\textsf{\dfrac{\phantom{ }}{\phantom{ }}}", Midpoint[PosTable + ((4 * spalte), (-zeile1) - zeile2), PosTable + ((4 * spalte), (-zeile1) - zeile2 - zeile3)] + (disTable, 0), false, true, 1, 0) → txtF74
  34. Text("\textsf{\dfrac{\phantom{ }}{\phantom{ }}}", Midpoint[PosTable + ((5 * spalte), (-zeile1) - zeile2), PosTable + ((5 * spalte), (-zeile1) - zeile2 - zeile3)] + (disTable, 0), false, true, 1, 0) → txtF75
  35. Textfield(inputF721) → InputBoxF721
  36. Textfield(inputF722) → InputBoxF722
  37. Textfield(inputF731) → InputBoxF731
  38. Textfield(inputF732) → InputBoxF732
  39. Textfield(inputF741) → InputBoxF741
  40. Textfield(inputF742) → InputBoxF742
  41. Textfield(inputF751) → InputBoxF751
  42. Textfield(inputF752) → InputBoxF752
  43. If(step ≟ 2, animationDice ≟ 0 ∨ animationDice ≟ endDice, true) → clickableBtnBack
  44. If(step ≟ 3, (0.4, -0.6), step ≟ 6 ∧ (¬correct061), (10, 6.1), step ≟ 6 ∧ correct061, (10, 3.5), (12, 0.5)) → PosBtnSolution