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Monty Hall Problem Demonstration by Alkeos Souyoul

Monty Hall Problem Demonstration by Alkeos Souyoul
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2019-05-17 06:15
Probability & StatisticsGeometric ConstructionSlider Animation
This example demonstrates the classic Monty Hall problem by simulating a door-switching game to illustrate probability variations. It involves core math concepts like probability & statistics, logical reasoning, and decision analysis. Construction highlights include using GeoGebra commands/objects such as Element, Point, OrthogonalLine, Intersect, Midpoint, Line, Circle, Vector to build the game scenario and interactive elements. Suitable for high school and above learners to understand counterintuitive phenomena in probability theory and model construction.

GeoGebra Commands & Parameters

  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