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概率与树形图（复制版）

概率与树形图（复制版）
几何画板及绘图内容加载中，请稍等……
2016-04-29 17:09
数列概率统计几何作图滑块动画函数图像
该范例通过动态树形图直观展示概率计算过程，演示了如何利用分支结构表示随机试验的多种结果及其概率。核心数学概念包括条件概率、独立事件、概率乘法法则以及树形图的构建。作图要点：使用GeoGebra的Sequence命令生成序列，Center和Point定位节点，Segment连接分支，If条件判断控制显示，并涉及多个对象如C21bY、C21bX等坐标变量，以及BallRadius、TotalBallNo等参数用于模拟球类抽取实验。适合中学阶段（初中高年级至高中）的概率统计教学，也可用于大学入门课程，帮助学生理解复杂概率问题的可视化分解。

GeoGebra 命令及参数

  1. Sequence(Circle[Element[Centre01, i], BallRadius], i, 2, NoB + 1) → BallBlueList01
  2. Center(Element[BallBlueList01, 1]) → AA
  3. Sequence(Circle[Element[Centre11, i], BallRadius], i, 2, NoB) → BallBlueList11
  4. Sequence(Circle[Element[Centre12, i], BallRadius], i, 2, NoB + 1) → BallBlueList12
  5. Sequence(Circle[Element[Centre21, i], BallRadius], i, 2, NoB - 1) → BallBlueList21
  6. Sequence(Circle[Element[Centre22, i], BallRadius], i, 2, NoB) → BallBlueList22
  7. Sequence(Circle[Element[Centre24, i], BallRadius], i, 2, NoB + 1) → BallBlueList24
  8. Sequence(Circle[Element[Centre23, i], BallRadius], i, 2, NoB) → BallBlueList23
  9. Sequence(If[step ≤ 10, (FindCor(step, 0, 10, x(Element[Tree01Point, i]), x(Element[Tree02Point, i])), FindCor(step, 0, 10, y(Element[Tree01Point, i]), y(Element[Tree02Point, i]))), Element[Tree02Point, i]], i, 1, 2) → Tree02MovingPoint
  10. Sequence(Segment[Element[Tree01Point, i], Element[Tree02MovingPoint, i]], i, 1, 2) → TreeLine01
  11. Sequence(If[step < 35, Element[Tree03Point, i], If[step > 45, Element[Tree04Point, i], (FindCor(step, 35, 45, x(Element[Tree03Point, i]), x(Element[Tree04Point, i])), FindCor(step, 35, 45, y(Element[Tree03Point, i]), y(Element[Tree04Point, i])))]], i, 1, 4) → Tree04MovingPoint
  12. Sequence(Segment[Element[Tree03Point, i], Element[Tree04MovingPoint, i]], i, 1, 4) → TreeLine02
  13. If(step < 20, Element[Centre11, NoB + 1], If[step > 30, C11a, (FindCor(step, 20, 30, x(Element[Centre11, NoB + 1]), x(C11a)), FindCor(step, 20, 30, y(Element[Centre11, NoB + 1]), y(C11a)))]) → C11aMove
  14. If(step < 20, Element[Centre12, NoB + 2], If[step > 30, C12a, (FindCor(step, 20, 30, x(Element[Centre12, NoB + 2]), x(C11a)), FindCor(step, 20, 30, y(Element[Centre12, NoB + 2]), y(C12a)))]) → C12aMove
  15. If(step < 50, Element[Centre21, NoB], If[step > 60, C21b, (FindCor(step, 50, 60, x(Element[Centre21, NoB]), x(C21b)), FindCor(step, 50, 60, y(Element[Centre21, NoB]), y(C21b)))]) → C21bMove
  16. If(step < 50, Element[Centre23, NoB + 1], If[step > 60, C23b, (FindCor(step, 50, 60, x(Element[Centre23, NoB + 1]), x(C23b)), FindCor(step, 50, 60, y(Element[Centre23, NoB + 1]), y(C23b)))]) → C23bMove
  17. If(step < 50, Element[Centre24, NoB + 3], If[step > 60, C24b, (FindCor(step, 50, 60, x(Element[Centre24, NoB + 3]), x(C24b)), FindCor(step, 50, 60, y(Element[Centre24, NoB + 3]), y(C24b)))]) → C24bMove
  18. If(step < 50, Element[Centre22, nb + 1], If[step > 60, C22b, (FindCor(step, 50, 60, x(Element[Centre22, nb + 1]), x(C22b)), FindCor(step, 50, 60, y(Element[Centre22, nb + 1]), y(C22b)))]) → C22bMove
  19. Sequence(Circle[Element[BlueSelectedMovingCentreList, i], BallRadius], i, 1, 1) → BallBlueSelectedList01
  20. Sequence(Circle[Element[RedSelectedMovingCentreList, i], BallRadius], i, 2, 5) → BallRedSelectedList02
  21. Sequence(Circle[Element[RedSelectedMovingCentreList, i], BallRadius], i, 1, 1) → BallRedSelectedList01
  22. Sequence(Circle[Element[BlueSelectedMovingCentreList, i], BallRadius], i, 2, 5) → BallBlueSelectedList02
  23. Sequence(Circle[Element[Centre01, i], BallRadius], i, NoB + 2, nb + 1) → BallRedList01
  24. Sequence(Circle[Element[Centre11, i], BallRadius], i, NoB + 2, nb + 1) → BallRedList11
  25. Sequence(Circle[Element[Centre12, i], BallRadius], i, NoB + 3, nb + 1) → BallRedList12
  26. Sequence(Circle[Element[Centre22, i], BallRadius], i, NoB + 2, nb) → BallRedList22
  27. Sequence(Circle[Element[Centre23, i], BallRadius], i, NoB + 3, nb + 1) → BallRedList23
  28. Sequence(Circle[Element[Centre24, i], BallRadius], i, NoB + 4, nb + 1) → BallRedList24
  29. Sequence(Circle[Element[Centre21, i], BallRadius], i, NoB + 2, nb + 1) → BallRedList21
  30. Point(tempL11) → Z17
  31. Segment(Z17, Z08) → i

AI 绘图提示语参考

画一个动态的树形图来展示概率计算，包含多个分支结构代表随机实验的不同结果及其概率。图中应显示多个蓝色和红色的球，分布在树的不同节点上，部分节点会随时间变化位置。树的第一层有2个分支，第二层有4个分支，第三层有2个分支，每个分支上都有若干个球。树的结构应清晰展示概率的传递和分支的选择过程，适合用于教学演示概率和统计概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。