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概率统计：幸运轮盘的概率问题

概率统计：幸运轮盘的概率问题
几何画板及绘图内容加载中，请稍等……
2024-06-19 17:24
概率统计几何作图函数图像
所属专题 Wahrscheinlichkeitsrechnung - Einführung
①本范例通过GeoGebra演示幸运轮盘的概率计算与决策分析；②涉及核心数学概念：概率、可能性大小比较、统计规律；③构造摘要中用到了Circle（圆）、CircleSector（扇形）、Point（点）、Textfield（文本框）、Sequence（序列）等命令和对象；④适合初中七、八年级学生，用于概率统计教学和实践活动。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {1, 3, 10, 3, 3, 8, 8, 9, 2, 7}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. Circle(MP, radius) → glücksrad1
  5. Circle(MP, radius + 0.3) → glücksrad2
  6. 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
  7. Sequence(MP + (radius * (cos(360° - k°), sin(360° - k°))), k, 0, 1079) → PGRList
  8. Point(PGRList) → PosGR0
  9. CircleSector(MP, PosGR1, PosGR8) → sek1
  10. CircleSector(MP, PosGR2, PosGR1) → sek2
  11. CircleSector(MP, PosGR3, PosGR2) → sek3
  12. CircleSector(MP, PosGR4, PosGR3) → sek4
  13. CircleSector(MP, PosGR5, PosGR4) → sek5
  14. CircleSector(MP, PosGR6, PosGR5) → sek6
  15. CircleSector(MP, PosGR7, PosGR6) → sek7
  16. CircleSector(MP, PosGR8, PosGR7) → sek8
  17. If(index1 < 360, 3, (-2.55 / (end1 - 360) * index1) + 3 + (2.55 * 360 / (end1 - 360))) → speed
  18. mean(Unique[RemoveUndefined[Sequence[IndexOf[true, SektorZeiger, k], k, 1, Length[SektorZeiger]]]]) → posSektor1
  19. PolyLine({PosSB, Corner[txt031, 1] + (0.5 * (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] + (0.5 * (Corner[txt031, 4] - Corner[txt031, 1])) + (0, 0.5), PosSB}) → sb03
  20. Point(PGRList) → PosGS0
  21. CircleSector(MP, PosGS1, PosGS7) → sek51
  22. CircleSector(MP, PosGS2, PosGS1) → sek52
  23. CircleSector(MP, PosGS3, PosGS2) → sek53
  24. CircleSector(MP, PosGS4, PosGS3) → sek54
  25. CircleSector(MP, PosGS5, PosGS4) → sek55
  26. CircleSector(MP, PosGS6, PosGS5) → sek56
  27. CircleSector(MP, PosGS7, PosGS6) → sek57
  28. Join({Sequence[MP + ((2 * radius / 3) * (cos(((-index2))° - (360° * (Sum[einteilung2, k] - einteilung2(k) / 2) / Sum[einteilung2])), sin(((-index2))° - (360° * (Sum[einteilung2, k] - einteilung2(k) / 2) / Sum[einteilung2])))), k, 1, Length[einteilung2]] + (-0.5, 0.48), Reverse[Sequence[StartStar + (k * (MP + ((-radius) - 1, 0) - StartStar)), k, 0, 1, 0.05]]}) → PosStarList
  29. Point(PosStarList) → PosStar
  30. Polygon(PosStar, PosStar + (1, 0), PosStar + (1, -0.96), PosStar + (0, -0.96)) → polyStar, posstar, f, g, h
  31. IndexOf(PosStar, PosStarList) → StarIndex
  32. PolyLine({PosSB, Corner[txt052, 1] + (0.5 * (Corner[txt052, 4] - Corner[txt052, 1])), Corner[txt052, 1], Corner[txt052, 2] + (0.2, 0), Corner[txt052, 3] + (0.2, 0.15), Corner[txt052, 4] + (0, 0.15), Corner[txt052, 1] + (0.5 * (Corner[txt052, 4] - Corner[txt052, 1])) + (0, 0.5), PosSB}) → sb052
  33. If(index2 < 360, 3, (-2.55 / (end2 - 360) * index2) + 3 + (2.55 * 360 / (end2 - 360))) → speed2
  34. PolyLine({PosSB, Corner[txt061, 1] + (0.5 * (Corner[txt061, 4] - Corner[txt061, 1])), Corner[txt061, 1], Corner[txt061, 2] + (0.2, 0), Corner[txt061, 3] + (0.2, 0.15), Corner[txt061, 4] + (0, 0.15), Corner[txt061, 1] + (0.5 * (Corner[txt061, 4] - Corner[txt061, 1])) + (0, 0.5), PosSB}) → sb06
  35. mean(Unique[RemoveUndefined[Sequence[IndexOf[true, SektorZeiger2, k], k, 1, Length[SektorZeiger2]]]]) → posSektor2
  36. If(step ≟ 3, gedreht1 ∧ posSektor1 ≟ 1 ∧ index1 ≟ end1, step ≟ 4, option41, step ≟ 5, StarIndex ≟ 2 ∧ showFB5, step ≟ 6, gedreht2 ∧ posSektor2 ≟ 2 ∧ index2 ≟ end2, true) → clickableBtnNext
  37. Remove(721…1080, Sequence[(k * 45), k, 1, 40]) → RandomList
  38. PolyLine({PosSB, Corner[txt011, 1] + (0.25 * (Corner[txt011, 4] - Corner[txt011, 1])), Corner[txt011, 1] + (0, -0.2), Corner[txt011, 2] + (0.2, -0.2), 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, 0.5), PosSB}) → sb01
  39. PolyLine({PosSB, Corner[txt021, 1] + (0.4 * (Corner[txt021, 4] - Corner[txt021, 1])), Corner[txt021, 1], Corner[txt021, 2] + (0.2, 0), Corner[txt021, 3] + (0.2, 0.15), Corner[txt021, 4] + (0, 0.15), Corner[txt021, 1] + (0.5 * (Corner[txt021, 4] - Corner[txt021, 1])) + (0, 0.5), PosSB}) → sb02
  40. PolyLine({PosSB, Corner[txt051, 1] + (0.4 * (Corner[txt051, 4] - Corner[txt051, 1])), Corner[txt051, 1], Corner[txt051, 2] + (0.2, 0), Corner[txt051, 3] + (0.2, 0.15), Corner[txt051, 4] + (0, 0.15), Corner[txt051, 1] + (0.5 * (Corner[txt051, 4] - Corner[txt051, 1])) + (0, 0.5), PosSB}) → sb05
  41. If(step ≟ 3, ¬drehen, true) → clickableBtnBack
  42. Join({Sequence[MP + ((2 * radius / 3) * (cos((-(index1°)) - (360° * (Sum[einteilung1, k] - einteilung1(k) / 2) / Sum[einteilung1])), sin((-(index1°)) - (360° * (Sum[einteilung1, k] - einteilung1(k) / 2) / Sum[einteilung1])))), k, 1, Length[einteilung1]] + (-0.5, 0.48), Reverse[Sequence[StartStar + (k * (MP + ((-radius) - 1, 0) - StartStar)), k, 0, 1, 0.05]]}) → PosStarList1
  43. Text("\textsf{\bold{Zieh mich!}}", MP + ((1.65 * radius) * (cos(((-index2))°), sin(((-index2))°))), false, true, 0, 0) → text8
  44. Text("\textsf{\bold{Zieh mich!}}", MP + ((1.35 * radius) * (cos((-(index1°))), sin((-(index1°))))), false, true, 0, 0) → text7
  45. Angle(MP + (1, 0), MP, PosGR0) → Angle03
  46. CircleArc(MP, PosArc, PosGR0) → arc03
  47. Segment(PosArc, PosArc + (0.01 * UnitVector[Tangent[PosArc, glücksrad1]])) → arrow03
  48. Angle(MP + (1, 0), MP, PosGS0) → Angle07
  49. CircleArc(MP, PosArc07, PosGS0) → arc07
  50. Segment(PosArc07, PosArc07 + (0.01 * UnitVector[Tangent[PosArc07, glücksrad1]])) → arrow07

AI 绘图提示语参考

这是一个彩票轮盘图形，中心有一个点，周围分布着多个扇形区域。扇形之间有间隔，形成一个圆形结构。图形中包含一个较大的主圆和一个小圆，以及一些星星图案。扇形区域之间可能标注有文本提示。整体图形用于概率计算和决策分析，扇形的大小和数量可以表示不同结果的概率。图形布局清晰，便于理解概率分布。
以上提示语为根据原始绘图命令整理而来，仅供参考。