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概率模拟：弹珠抽取与频率分布动态演示

概率模拟：弹珠抽取与频率分布动态演示
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2019-07-02 07:06
函数数列概率统计滑块动画函数图像
该范例通过GeoGebra动态模拟从多色弹珠集合中随机抽取的过程，直观展示频率与概率的关系。核心数学概念包括概率统计中的随机事件、频率分布、比值计算以及算术运算（如加减法）。作图要点：利用RandomDiscrete和Random命令生成随机抽取结果，Frequency和Unique统计各颜色出现次数，BarChart绘制频率柱状图，TableText生成数据表格，并通过按钮（button2、RESET、STOP）和滑块（speed）控制模拟速度与重置。对象包括Marbles（弹珠）、Red1至Green6等颜色变量，以及dlist、NumTwos、NumOnes等统计列表。适合中学数学概率统计教学，帮助学生理解大数定律与频率稳定于概率的直观现象，也可用于探究随机性与样本量的关系。

GeoGebra 命令及参数

  1. Frequency({2, 2}, dlist) → Twos
  2. Element(Twos, 1) → NumTwos
  3. Frequency({1, 1}, dlist) → Ones
  4. Element(Ones, 1) → NumOnes
  5. Unique(dlist) → list1
  6. Frequency(dlist) → dfreq
  7. If(dlist ≟ {}, 0.1, Sum[dfreq]) → sum
  8. Random(0, Marbles - 1) → Red1
  9. Random(0, Marbles - Red1) → Blue2
  10. Random(0, Marbles - Blue2 - Red1) → Yellow3
  11. Random(0, Marbles - Yellow3 - Blue2 - Red1) → Black4
  12. Random(0, Marbles - Black4 - Yellow3 - Blue2 - Red1) → White5
  13. BarChart(dlist, 0.8) → b
  14. Append(row1, "TOTAL") → row1a
  15. Append(row2, sum) → row2a
  16. TableText({row1a, row2a}, "c_") → text2
  17. Random(0, Marbles - 1) → a
  18. Random(0, Marbles - 1) → c
  19. Random(0, Marbles - 1) → d
  20. Random(0, Marbles - 1) → e
  21. Random(0, Marbles - 1) → f
  22. Random(0, Marbles - 1) → g
  23. Random(0, Marbles - 1) → h
  24. Random(0, Marbles - 1) → i
  25. Random(0, Marbles - 1) → j
  26. Random(0, Marbles - 1) → k
  27. TableText({row0, row1, row2, row3, row4, row5, row6}, "c_") → Answers
  28. RandomDiscrete({1, 2, 3, 4, 5, 6}, {1 / 6, 1 / 6, 1 / 6, 1 / 6, 1 / 6, 1 / 6}) → Outcome1
  29. Frequency({3, 3}, dlist) → Threes
  30. Frequency({4, 4}, dlist) → Fours
  31. Frequency({5, 5}, dlist) → Fives
  32. Frequency({6, 6}, dlist) → Sixes
  33. Element(Threes, 1) → NumThrees
  34. Element(Fours, 1) → NumFours
  35. Element(Fives, 1) → NumFives
  36. Element(Sixes, 1) → NumSixes
  37. Text(NumOnes) → text13
  38. Text(NumTwos) → text14
  39. Text(NumThrees) → text15
  40. Text(NumFours) → text16
  41. Text(NumFives) → text17
  42. Text(NumSixes) → text18
  43. Text(FreqOne) → text19
  44. Text(FreqTwo) → text20
  45. Text(FreqThree) → text21
  46. Text(FreqFour) → text22
  47. Text(FreqFive) → text23
  48. Text(FreqSix) → text24
  49. Text(("Total = " * sum)) → text27