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Extraction, Frequencies and Probabilities of a Ballot Box

Extraction, Frequencies and Probabilities of a Ballot Box
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2020-01-10 05:10
VectorSequenceSolid GeometryProbability & StatisticsSlider Animation
This GeoGebra example demonstrates the relationship between empirical frequencies and theoretical probabilities when drawing balls from a three-dimensional ballot box (cuboid). It visually shows how the observed frequency of each outcome converges to the theoretical probability as the number of trials increases, illustrating the law of large numbers. Core concepts include probability, frequency, hypothesis testing, exponential functions, and 3D geometry with vectors. The construction uses commands such as Polygon, Circle, Sequence, First, CountIf, Element, Point, Segment, and Vector to build the cuboid, balls, and dynamic counters. A slider (Speed) controls the number of extractions, and the interface displays frequency counts and probability comparisons. Suitable for high school or introductory college statistics courses, this interactive tool helps students grasp the difference between empirical and theoretical probability and supports discussions on hypothesis testing and random sampling.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Create a 3D cuboid ballot box containing six colored spheres, each representing one of six possible outcomes. The box is constructed from multiple polygonal faces with edges and vertices. In front or beside the box, build a dynamic statistical chart using circles and segments to display the frequency of each outcome and compare it with theoretical probabilities. Include a slider to control the number of draws, and highlight the drawn sphere each time. The overall layout should clearly show the random drawing process, cumulative frequencies, and convergence of empirical frequencies to theoretical probabilities, emphasizing the relationship between observed and expected outcomes.
The prompt above was compiled from the original drawing commands and is for reference only.