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识别随机试验

识别随机试验
几何画板及绘图内容加载中，请稍等……
2024-06-19 17:24
概率统计几何作图
所属专题 Wahrscheinlichkeitsrechnung - Einführung
本范例通过多个选择题和开放题，帮助学生识别随机试验的特征。核心数学概念包括随机试验的定义和条件。使用了GeoGebra命令如Sequence, Element, Textfield等。适合初中7-8年级学生学习概率统计。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {10, 10, 7, 8, 10, 8, 6, 9, 8, 2}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. Random(10, 30) → endDice
  5. PolyLine({PosSB1, Corner[txt011, 1] + (0.25 * (Corner[txt011, 4] - Corner[txt011, 1])), Corner[txt011, 1], Corner[txt011, 2] + (0.2, 0), Corner[txt011, 3] + (0.2, 0.15), Corner[txt011, 4] + (0, 0.15), Corner[txt011, 1] + (0.25 * (Corner[txt011, 4] - Corner[txt011, 1])) + (0, 0.75), PosSB1}) → sb011
  6. Sequence(MPAuswahl + (radiusAuswahl * (cos(90° + (k * (360°) / 5)), sin(90° + (k * (360°) / 5)))), k, 0, 4) → MPList
  7. Circle(MPList(1), radiusSymbol) → CSymbol1
  8. Circle(MPList(2), radiusSymbol) → CSymbol2
  9. Circle(MPList(3), radiusSymbol) → CSymbol3
  10. Circle(MPList(4), radiusSymbol) → CSymbol4
  11. Circle(MPList(5), radiusSymbol) → CSymbol5
  12. PolyLine({PosSB, Corner[txt121, 1] + (0.25 * (Corner[txt121, 4] - Corner[txt121, 1])), Corner[txt121, 1], Corner[txt121, 2] + (0.2, 0), Corner[txt121, 3] + (0.2, 0.15), Corner[txt121, 4] + (0, 0.15), Corner[txt121, 1] + (0.25 * (Corner[txt121, 4] - Corner[txt121, 1])) + (0, 0.75), PosSB}) → sb121
  13. Invert(pixMat) → invPixMat
  14. Textfield(input131) → InputBox131
  15. PolyLine({PosSB, Corner[txt031, 1] + (0.25 * (Corner[txt031, 4] - Corner[txt031, 1])), Corner[txt031, 1], Corner[txt031, 2] + (0.2, 0), Corner[txt031, 3] + (0.2, 0.15), Corner[txt031, 4] + (0, 0.15), Corner[txt031, 1] + (0.25 * (Corner[txt031, 4] - Corner[txt031, 1])) + (0, 0.75), PosSB}) → sb031
  16. CircleSector(MP + (0, radius - 0.3), MP + (0, radius - 0.3) + (0.6 * (cos(80°), sin(80°))), MP + (0, radius - 0.3) + (0.6 * (cos(100°), sin(100°)))) → zeiger
  17. Circle(MP, radius) → glücksrad1
  18. Circle(MP, (radius * 1.13)) → glücksrad2
  19. Sequence(MP + (radius * (cos(360° - k°), sin(360° - k°))), k, 0, 1079) → PGRList
  20. Point(PGRList) → PosGR0
  21. If(index1 < 360, 3, (-2.55 / (end1 - 360) * index1) + 3 + (2.55 * 360 / (end1 - 360))) → speed
  22. PolyLine({PosSB, Corner[txt221, 1] + (0.25 * (Corner[txt221, 4] - Corner[txt221, 1])), Corner[txt221, 1], Corner[txt221, 2] + (0.2, 0), Corner[txt221, 3] + (0.2, 0.15), Corner[txt221, 4] + (0, 0.15), Corner[txt221, 1] + (0.25 * (Corner[txt221, 4] - Corner[txt221, 1])) + (0, 0.75), PosSB}) → sb221
  23. Circle(MPmini, radiusmini) → grmini1
  24. Circle(MPmini, (radiusmini * 1.13)) → grmini2
  25. CircleSector(MPmini + (0, radiusmini - (0.3 / radiusmini * 2.25)), MPmini + (0, radiusmini - (0.3 / radiusmini * 2.25)) + (0.7 * (cos(80°), sin(80°))), MPmini + (0, radiusmini - (0.3 / radiusmini * 2.25)) + (0.7 * (cos(100°), sin(100°)))) → zeigermini
  26. PolyLine({PosSB, Corner[txt321, 1] + (0.25 * (Corner[txt321, 4] - Corner[txt321, 1])), Corner[txt321, 1], Corner[txt321, 2] + (0.2, 0), Corner[txt321, 3] + (0.2, 0.15), Corner[txt321, 4] + (0, 0.15), Corner[txt321, 1] + (0.25 * (Corner[txt321, 4] - Corner[txt321, 1])) + (0, 0.75), PosSB}) → sb321
  27. PolyLine({PosSB, Corner[txt421, 1] + (0.25 * (Corner[txt421, 4] - Corner[txt421, 1])), Corner[txt421, 1], Corner[txt421, 2] + (0.2, 0), Corner[txt421, 3] + (0.2, 0.15), Corner[txt421, 4] + (0, 0.15), Corner[txt421, 1] + (0.25 * (Corner[txt421, 4] - Corner[txt421, 1])) + (0, 0.75), PosSB}) → sb421
  28. PolyLine({PosSB, Corner[txt521, 1] + (0.25 * (Corner[txt521, 4] - Corner[txt521, 1])), Corner[txt521, 1], Corner[txt521, 2] + (0.2, 0), Corner[txt521, 3] + (0.2, 0.15), Corner[txt521, 4] + (0, 0.15), Corner[txt521, 1] + (0.25 * (Corner[txt521, 4] - Corner[txt521, 1])) + (0, 0.75), PosSB}) → sb521
  29. Textfield(input531) → InputBox531
  30. RandomElement({1, 2}) → valueCoin
  31. Point(Segment[PosAnimationCoin1, PosAnimationCoin1 + (0, 0.15)]) → PosCoinA1
  32. If(step5 ≟ 3, (5.325, -0.84), (0.5, 2)) → PosImgCoins1
  33. PolyLine({PosSB, Corner[txt231, 1] + (0.25 * (Corner[txt231, 4] - Corner[txt231, 1])), Corner[txt231, 1], Corner[txt231, 2] + (0.2, 0), Corner[txt231, 3] + (0.2, 0.15), Corner[txt231, 4] + (0, 0.15), Corner[txt231, 1] + (0.25 * (Corner[txt231, 4] - Corner[txt231, 1])) + (0, 0.5), PosSB}) → sb231
  34. PolyLine({PosSB, Corner[txt331, 1] + (0.25 * (Corner[txt331, 4] - Corner[txt331, 1])), Corner[txt331, 1], Corner[txt331, 2] + (0.2, 0), Corner[txt331, 3] + (0.2, 0.15), Corner[txt331, 4] + (0, 0.15), Corner[txt331, 1] + (0.25 * (Corner[txt331, 4] - Corner[txt331, 1])) + (0, 0.5), PosSB}) → sb331
  35. PolyLine({PosSB, Corner[txt431, 1] + (0.25 * (Corner[txt431, 4] - Corner[txt431, 1])), Corner[txt431, 1], Corner[txt431, 2] + (0.2, 0), Corner[txt431, 3] + (0.2, 0.15), Corner[txt431, 4] + (0, 0.15), Corner[txt431, 1] + (0.25 * (Corner[txt431, 4] - Corner[txt431, 1])) + (0, 0.5), PosSB}) → sb431
  36. Random(1, 6) → valueDice
  37. Sequence(Random[1, 11], m, 1, endDice) → RotateDiceList, {8, 3, 7, 9, 10, 7, 11, 11, 10, 1, 4, 11, 5, 6, 2, 7, 11, 4, 11, 8, 9, 10, 9, 3, 5, 6, 3, 3, 9, 5}
  38. If(animationDice ≟ 0, 0, RotateDiceList(animationDice)) → showDR
  39. Corner(imgSlot1, 3) → PosImgSlot3
  40. Point(PosSlot) → PSlot
  41. IndexOf(PSlot, PosSlot) → posPSlot
  42. RandomElement(0…9) → SlotN1
  43. RandomElement(0…9) → SlotN2
  44. RandomElement(0…9) → SlotN3
  45. Join({0…9, 0…9, 0…9}) → ListReference
  46. RandomElement(0…9) → SlotN12
  47. RandomElement(0…9) → SlotN22
  48. RandomElement(0…9) → SlotN32
  49. Zip(Element[ListReference, m], m, Sequence[IndexOf[SlotN1, ListReference], IndexOf[SlotN12, ListReference] + If[SlotN12 - SlotN1 ≤ 5, 20, 10]]) → ListSN1
  50. Zip(Element[ListReference, m], m, Sequence[IndexOf[SlotN2, ListReference], IndexOf[SlotN22, ListReference] + If[SlotN22 - SlotN2 ≤ 5, 20, 10]]) → ListSN2
  51. Zip(Element[ListReference, m], m, Sequence[IndexOf[SlotN3, ListReference], IndexOf[SlotN32, ListReference] + If[SlotN32 - SlotN3 ≤ 5, 20, 10]]) → ListSN3
  52. Zip(Text[(("\textsf\Huge{" * ReplaceAll["" + (k) + "", ".", ","]) * "}"), PosSlotN1 + (0, (m * absSlotY) - ((animSlot1 * (Length[ListSN1] - 1)) * absSlotY)), true, true, 0, 0], m, Sequence[0, Length[ListSN1]], k, ListSN1) → TxtSlot1
  53. Zip(Text[(("\textsf\Huge{" * ReplaceAll["" + (k) + "", ".", ","]) * "}"), PosSlotN2 + (0, (m * absSlotY) - ((animSlot2 * (Length[ListSN2] - 1)) * absSlotY)), true, true, 0, 0], m, Sequence[0, Length[ListSN2]], k, ListSN2) → TxtSlot2
  54. Zip(Text[(("\textsf\Huge{" * ReplaceAll["" + (k) + "", ".", ","]) * "}"), PosSlotN3 + (0, (m * absSlotY) - ((animSlot3 * (Length[ListSN3] - 1)) * absSlotY)), true, true, 0, 0], m, Sequence[0, Length[ListSN3]], k, ListSN3) → TxtSlot3
  55. Polygon(PolySlotP1, PolySlotP2, PolySlotP3, (x(PolySlotP1), y(PolySlotP3))) → PolySlot, polyslotp1, polyslotp2, polyslotp3, polyslotp4
  56. If(step4 ≟ 3, (-0.5, -3.22), (-0.5, 0)) → PosImgSlotEnd1
  57. Corner(imgSlotEnd, 3) → PosImgSlotEnd3
  58. RandomElement({1, 2, 3}) → Kugel
  59. Circle(PosKugel1, radiusKugel) → Kugel1
  60. Circle(PosKugel2, radiusKugel) → Kugel2
  61. Circle(PosKugel3, radiusKugel) → Kugel3
  62. RandomElement({1, 2, 3}) → KugelZahl
  63. Text((("\textsf{\Huge{" * KugelZahl) * "}}"), PosKugelEnd, false, true, 0, 0) → txtKugelZahl
  64. Circle(PosKugel1, radiusKugel) → KugelRand1
  65. Circle(PosKugel2, radiusKugel) → KugelRand2
  66. Circle(PosKugel3, radiusKugel) → KugelRand3
  67. If(Task ≟ 1 ∧ step1 ≟ 1, animationDice ≟ 0 ∨ animationDice ≟ endDice, true, Task ≟ 5 ∧ step5 ≟ 1, animationCoin ≟ 0 ∨ animationCoin ≟ 11, Task ≟ 2 ∧ step2 ≟ 1, ¬drehen, Task ≟ 4 ∧ step4 ≟ 1, animSlot1 ∈ {0, 1} ∧ animSlot2 ∈ {0, 1} ∧ animSlot3 ∈ {0, 1}, Task ≟ 3 ∧ step3 ≟ 1, animKugel ∈ {0, 1}) → clickableBtnBack
  68. If(Task ≟ 4 ∧ step4 ≟ 3, correct431, Task ≟ 1 ∧ step1 ≟ 3, correct131, Task ≟ 5 ∧ step5 ≟ 3, correct531, Task ≟ 2 ∧ step2 ≟ 1, gedreht1 ∧ (¬drehen) ∧ (¬drehbar), Task ≟ 4 ∧ step4 ≟ 1, EndSlot, Task ≟ 3 ∧ step3 ≟ 1, animKugel ≟ 1, Task ≟ 0 ∧ step ≟ 2, Task ≟ 2 ∧ step2 ≟ 3, correct231, true, selected1 ∨ selected2 ∨ selected3 ∨ selected4 ∨ selected5, Task ≟ 1 ∧ step1 ≟ 1, animationDice ≟ endDice, Task ≟ 5 ∧ step5 ≟ 1, animationCoin ≟ 11, Task ≟ 1 ∧ step1 ≟ 2 ∨ Task ≟ 2 ∧ step2 ≟ 2 ∨ Task ≟ 3 ∧ step3 ≟ 2 ∨ Task ≟ 4 ∧ step4 ≟ 2 ∨ Task ≟ 5 ∧ step5 ≟ 2, correctO ∧ validate) → clickableBtnNext
  69. If(step3 ≟ 3, (11.845, -1.54), (1, 0.5)) → PosImgGlasEnd1
  70. If(step1 ≟ 3, (5.625, -1.72), (0.5, 1)) → PosImgWürfelEnd1
  71. Textfield(input231) → InputBox231
  72. Sector(sek1, CP1, CP2) → sekG1
  73. Sector(sek1, CP2, CP3) → sekG2
  74. Sector(sek1, CP3, CP4) → sekG3
  75. Sector(sek1, CP4, CP1) → sekG4
  76. Remove(721…1080, Sequence[(k * 90), k, 1, 20]) → RandomList
  77. Sector(sekmini, MPmini + (radiusmini * (cos((-(index1°))), sin((-(index1°))))), MPmini + (radiusmini * (cos((-(index1°)) + 90°), sin((-(index1°)) + 90°)))) → sekGMini1
  78. Sector(sekmini, MPmini + (radiusmini * (cos(((-index1))° + 90°), sin(((-index1))° + 90°))), MPmini + (radiusmini * (cos(((-index1))° + 180°), sin(((-index1))° + 180°)))) → sekGMini2
  79. Sector(sekmini, MPmini + (radiusmini * (cos((-(index1°)) + 180°), sin((-(index1°)) + 180°))), MPmini + (radiusmini * (cos((-(index1°)) + 270°), sin((-(index1°)) + 270°)))) → sekGMini3
  80. Sector(sekmini, MPmini + (radiusmini * (cos(((-index1))° + 270°), sin(((-index1))° + 270°))), MPmini + (radiusmini * (cos(((-index1))°), sin(((-index1))°)))) → sekGMini4
  81. Circle(MPmini, (radiusmini * 1.13)) → grmini3
  82. PolyLine({PosSB, Corner[txt131, 1] + (0.35, 0), Corner[txt131, 2] + (0.2, 0), Corner[txt131, 3] + (0.2, 0.15), Corner[txt131, 4] + (0, 0.15), Corner[txt131, 1] + (0.25 * (Corner[txt131, 4] - Corner[txt131, 1])) + (0, 0.25), PosSB}) → sb131
  83. PolyLine({PosSB, Corner[txt531, 1] + (0.35, 0), Corner[txt531, 2] + (0.2, 0), Corner[txt531, 3] + (0.2, 0.15), Corner[txt531, 4] + (0, 0.15), Corner[txt531, 1] + (0.25 * (Corner[txt531, 4] - Corner[txt531, 1])) + (0, 0.25), PosSB}) → sb531
  84. PolyLine(MPList(3) + ((radiusSymbol + 0.1) * Sequence[(cos(k°), sin(k°)), k, 0, 360, 1])) → poly3
  85. PolyLine(MPList(4) + ((radiusSymbol + 0.1) * Sequence[(cos(k°), sin(k°)), k, 0, 360, 1])) → poly4
  86. PolyLine(MPList(5) + ((radiusSymbol + 0.1) * Sequence[(cos(k°), sin(k°)), k, 0, 360, 1])) → poly5
  87. PolyLine(MPList(1) + ((radiusSymbol + 0.1) * Sequence[(cos(k°), sin(k°)), k, 0, 360, 1])) → poly1
  88. PolyLine(MPList(2) + ((radiusSymbol + 0.1) * Sequence[(cos(k°), sin(k°)), k, 0, 360, 1])) → poly2
  89. Segment(Corner[imgCoinStart, 2] + (-3.6, 4.25), Corner[imgCoinStart, 2] + (-3.6, 4.25) + (0, 1)) → arrowCoin
  90. Text("\textsf{\bold{Zieh mich!}}", Point[arrowCoin, 0], false, true, 0, -1) → txtClickMe5
  91. Text("\textsf{\bold{Klick mich!}}", Midpoint[PosDiceA1, Corner[imgD1, 4]], false, true, -1, 0) → txtClickMe1
  92. Segment(PosClickMe3, PosClickMe3 + UnitVector[Vector[PosClickMe3, (1 / 3 * (PosKugel1 + PosKugel2 + PosKugel3))]]) → arrow3
  93. Text("\textsf{\bold{Klick mich!}}", PosClickMe3 + (-0.125, -0.125), false, true, 1, 1) → txtClickMe3
  94. Textfield(input431) → InputBox431
  95. Text("\bold{\textsf{Zieh mich!}}", PosGR0 + (1.25 * UnitVector[Vector[MP, PosGR0]]), false, true, 0, 0) → txtClickMe2
  96. Center(Circle[PosKugelStart1, PosKugelStart2, PosKugelStart3]) → PosMPMischen
  97. Distance(PosMPMischen, PosKugelStart1) → radiusMischen
  98. Sequence(Circle[PosKugelMischen(k), radiusKugel], k, 1, 3) → KugelMischen
  99. Sequence(Circle[PosKugelMischen(k), radiusKugel], k, 1, 3) → KugelMischenRand
  100. Segment(Midpoint[Corner[txtClickMe1, 2], Corner[txtClickMe1, 3]], Midpoint[Corner[txtClickMe1, 2], Corner[txtClickMe1, 3]] + (0.5, 0)) → segClickMe1
  101. LineBisector(PClickMe42, PClickMe41) → lineClickMe41
  102. Point(lineClickMe41) → PClickMe43
  103. Angle(MP + (1, 0), MP, PosGR0) → Angle02
  104. CircleArc(MP, PosArc02, PosGR0) → arc02
  105. Segment(PosArc02, PosArc02 + (0.01 * UnitVector[Tangent[PosArc02, glücksrad1]])) → arrow02
  106. Text("\textsf{\bold{Zieh mich!}}", PSlot + (0.25, 0.25), false, true, 1, 0) → txtClickMe4
  107. Mirror(CircleArc[PClickMe43, PClickMe41, PClickMe42], x = x(PClickMe41)) → arcClickMe4
  108. Mirror(Segment[PClickMe42, PClickMe42 - (0.01 * UnitOrthogonalVector[Vector[PClickMe42, PClickMe43]])], x = x(PClickMe41)) → segClickMe4

AI 绘图提示语参考

绘制一个交互式概率学习界面，包含多个随机实验的可视化装置。画面上方有一个随机数生成区，显示一排随机数字和一个文本输入框。中间是一个大转盘（幸运轮），由五个扇形区域组成，每个区域有一个圆形符号，中心有指针可旋转，转盘内外有两圈轨道。下面有三个并排的老虎机方框，每个框内显示一个随机数字（0-9）。右侧是掷骰子动画区，显示一个可旋转的骰子图案，下方有多个选项按钮。左侧是抛硬币实验区，显示一枚硬币的动画。整体布局错落有致，各实验装置之间有适当的间距，构成一个完整的概率统计学习工具界面。
以上提示语为根据原始绘图命令整理而来，仅供参考。