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蒙特霍尔问题演示

蒙特霍尔问题演示
几何画板及绘图内容加载中，请稍等……
2019-05-17 06:15
概率统计几何作图滑块动画
①本范例演示了经典的蒙特霍尔问题，通过模拟开关门游戏展示概率变化现象；②涉及的核心数学概念包括概率统计、逻辑推理和决策分析；③作图要点——从下方『构造摘要』提炼用到了Element, Point, OrthogonalLine, Intersect, Midpoint, Line, Circle, Vector等GeoGebra命令/对象构建游戏场景和交互元素；④适合高中及以上数学学习者，用于理解概率论中的反直觉现象和模型构建。

GeoGebra 命令及参数

  1. Element({1, 2, 3} \ {CarPos, door}, 1) → MontyDoor
  2. Point(xAxis) → A
  3. Point(xAxis) → B
  4. OrthogonalLine(A, xAxis) → a
  5. OrthogonalLine(B, xAxis) → b
  6. Point(a) → C
  7. OrthogonalLine(C, a) → c
  8. Intersect(b, c) → D
  9. Point(xAxis) → E
  10. OrthogonalLine(E, xAxis) → d
  11. Intersect(c, d) → F
  12. Midpoint(C, A) → G
  13. Midpoint(C, G) → H
  14. Midpoint(B, D) → I
  15. Midpoint(E, F) → J
  16. Midpoint(I, D) → K
  17. Midpoint(F, J) → L
  18. Line(A, B) → e
  19. Midpoint(G, A) → P
  20. Circle(C, P) → k
  21. Intersect(k, c, 1) → Q
  22. OrthogonalLine(Q, c) → j
  23. Circle(C, G) → h
  24. Intersect(h, a, 2) → O
  25. OrthogonalLine(O, a) → i
  26. Intersect(j, i) → R
  27. Vector(R, Q) → u
  28. OrthogonalLine(P, a) → f
  29. Intersect(b, f) → M
  30. Circle(D, M) → g
  31. Intersect(g, c, 1) → N
  32. OrthogonalLine(N, c) → l
  33. Intersect(i, l) → S
  34. Vector(S, N) → v
  35. Intersect(d, f) → T
  36. Circle(F, T) → p
  37. Intersect(p, c, 1) → U
  38. OrthogonalLine(U, c) → m
  39. Intersect(i, m) → V
  40. Vector(V, U) → w
  41. Circle(R, O) → q
  42. Intersect(q, i, 2) → Z
  43. Circle(Z, R) → r
  44. Intersect(r, i, 2) → W
  45. Intersect(b, i) → A_1
  46. Circle(S, A_1) → s
  47. Intersect(s, i, 2) → B_1
  48. Midpoint(O, R) → F_1
  49. Midpoint(Z, W) → G_1
  50. Circle(B_1, S) → t
  51. Intersect(t, i, 2) → H_1
  52. Midpoint(S, A_1) → I_1
  53. Midpoint(H_1, B_1) → J_1
  54. Intersect(d, i) → C_1
  55. Midpoint(V, C_1) → D_1
  56. Circle(V, C_1) → c_1
  57. Intersect(c_1, i, 2) → E_1
  58. Circle(E_1, V) → d_1
  59. Intersect(d_1, i, 2) → K_1
  60. Midpoint(E_1, K_1) → L_1
  61. Circle(A, G) → e_1
  62. Intersect(e_1, a, 1) → M_1
  63. OrthogonalLine(M_1, a) → n
  64. Intersect(j, n) → N_1
  65. Intersect(l, n) → O_1
  66. Intersect(m, n) → P_1
  67. Intersect(e, j) → Q_1
  68. Vector(N_1, Q_1) → z
  69. Intersect(e, l) → R_1
  70. Vector(O_1, R_1) → u_1
  71. Intersect(e, m) → S_1
  72. Vector(P_1, S_1) → v_1