投票箱抽取的频率与概率模拟

投票箱抽取的频率与概率模拟
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2020-01-10 05:10
该范例通过三维长方体(投票箱)和内部球体,动态演示从投票箱中抽取球体的频率与理论概率之间的关系。核心数学概念包括概率统计、频率与概率的对比、假设检验、指数函数以及三维向量与几何体。作图要点:使用GeoGebra的Polygon、Circle、Sequence、CountIf、Element、Point、Segment、Vector等命令构建三维投票箱和球体,并通过滑块(Speed)控制抽取次数,实时统计频率,同时用指数函数拟合或对比理论概率。适合高中及大学概率统计课程,用于直观理解大数定律和频率稳定于概率的现象,也可用于假设检验的演示。

GeoGebra 命令及参数

  1. Polygon(E, F, 4) → poly1, e_1, f_1, h, i, G, H
  2. Circle(C, 1) → k_1
  3. Circle(A, 1) → p
  4. Circle(AA, 1) → t
  5. Circle(I, 1) → c_1
  6. Circle(M, 1) → d_1
  7. Circle(J, 1) → g_1
  8. Sequence(Random[1, 6], i, 1, 1000) → liste1
  9. First(liste1, n) → Tirage
  10. CountIf(x ≟ 1, Tirage) → B3
  11. CountIf(x ≟ 2, Tirage) → B4
  12. CountIf(x ≟ 3, Tirage) → B5
  13. CountIf(x ≟ 4, Tirage) → B6
  14. CountIf(x ≟ 5, Tirage) → B7
  15. CountIf(x ≟ 6, Tirage) → B8
  16. Element(liste1, n) → dd
  17. Circle(O, 1) → e
  18. Circle(O, 1) → f
  19. Circle(O, 1) → g
  20. Circle(O, 1) → q
  21. Circle(O, 1) → r
  22. Circle(O, 1) → s
  23. Point(h) → P
  24. Point(h) → Q
  25. Segment(P, Q) → j
  26. Segment(R, S) → m
  27. Segment(R, T) → a_1
  28. Point(m) → U
  29. Point(m) → V
  30. Point(m) → W
  31. Point(m) → Z
  32. Point(m) → A_1
  33. Point(m) → B_1
  34. Point(m) → C_1
  35. Point(m) → D_1
  36. Point(m) → E_1
  37. Point(m) → F_1
  38. Polygon(U, V, I_1, G_1) → poly2, u, v, i_1, g_2
  39. Polygon(W, J_1, K_1, Z) → poly3, w, j_1, k_2, z
  40. Polygon(A_1, B_1, M_1, L_1) → poly4, a_2, b_1, m_1, l_1
  41. Polygon(N_1, O_1, D_1, C_1) → poly5, n_1, o_1, d_2, c_2
  42. Point(m) → P_1
  43. Point(m) → Q_1
  44. Polygon(E_1, F_1, S_1, R_1) → poly6, e_2, f_2, s_1, r_1
  45. Polygon(P_1, Q_1, U_1, T_1) → poly7, p_1, q_1, u_1, t_1
  46. Point(a_1) → H_1
  47. Point(a_1) → V_1
  48. Point(a_1) → W_1
  49. Point(a_1) → Z_1
  50. Point(a_1) → A_2
  51. Point(a_1) → B_2
  52. Point(a_1) → C_2
  53. Vector(R, T) → v_1
  54. Polygon(P_1, D_2, F_2, Q_1) → poly8, p_2, d_3, f_3, q_2
  55. Polygon(H_2, G_2, F_1, E_1) → poly9, h_2, g_3, f_4, e_3
  56. Polygon(J_2, I_2, D_1, C_1) → poly10, j_2, i_2, d_4, c_3
  57. Polygon(L_2, K_2, B_1, A_1) → poly11, l_2, k_3, b_2, a_3
  58. Polygon(N_2, M_2, Z, W) → poly12, n_2, m_2, z_1, w_1
  59. Polygon(P_2, O_2, V, U) → poly13, p_3, o_2, v_2, u_2
  60. Circle(Q_2, 1) → h_1
  61. Circle(R_2, 1) → r_2
  62. Circle(S_2, 1) → s_2
  63. Circle(T_2, 1) → t_2
  64. Circle(U_2, 1) → h_3
  65. Circle(V_2, 1) → q_3

AI 绘图提示语参考

绘制一个三维长方体投票箱,内部放置六个彩色球体,分别代表六种抽取结果。箱体由多个多边形面构成,每个面用线段和点定位。在箱体前方或侧面,用圆形和线段构建动态统计图表,显示每次抽取后各结果的频数与理论概率的对比。添加一个滑块控制抽取次数,并让每次抽取的球体高亮显示。整体布局需清晰展示随机抽取过程、频数累积和概率收敛趋势,强调经验频率与理论概率的关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。