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Long Run Probability

Long Run Probability
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2019-03-14 10:05
SequenceProbability & StatisticsGeometric Construction
This example demonstrates the concept of long-run probability through geometric and statistical visualization. Key mathematical concepts include median lines in geometry, algebraic subtraction, and binomial distribution. Construction involves GeoGebra commands like Element, If, Length, Intersect, and Sequence to create geometric objects and visualize data. Suitable for high school students or college freshmen to understand the intersection of probability and geometry.

GeoGebra Commands & Parameters

  1. Element(recordk, 1) → u_1
  2. If(u_1 ≟ n_1 ∨ u_1 ≟ n_2, 1, 0) → w_1
  3. Element(recordk, 2) → u_2
  4. If(u_2 ≟ n_1 ∨ u_2 ≟ n_2, 1, 0) → w_2
  5. Element(recordk, 20) → u_{20}
  6. Element(recordk, 18) → u_{18}
  7. Element(recordk, 16) → u_{16}
  8. Element(recordk, 14) → u_{14}
  9. Element(recordk, 12) → u_{12}
  10. Element(recordk, 10) → u_{10}
  11. Element(recordk, 8) → u_8
  12. Element(recordk, 6) → u_6
  13. Element(recordk, 5) → u_5
  14. Element(recordk, 4) → u_4
  15. Element(recordk, 3) → u_3
  16. Element(recordk, 7) → u_7
  17. Element(recordk, 9) → u_9
  18. Element(recordk, 11) → u_{11}
  19. Element(recordk, 13) → u_{13}
  20. Element(recordk, 15) → u_{15}
  21. Element(recordk, 17) → u_{17}
  22. Element(recordk, 19) → u_{19}
  23. If(u_{20} ≟ n_1 ∨ u_{20} ≟ n_2, 1, 0) → w_{20}
  24. If(u_{18} ≟ n_1 ∨ u_{18} ≟ n_2, 1, 0) → w_{18}
  25. If(u_{16} ≟ n_1 ∨ u_{16} ≟ n_2, 1, 0) → w_{16}
  26. If(u_{14} ≟ n_1 ∨ u_{14} ≟ n_2, 1, 0) → w_{14}
  27. If(u_{12} ≟ n_1 ∨ u_{12} ≟ n_2, 1, 0) → w_{12}
  28. If(u_{10} ≟ n_1 ∨ u_{10} ≟ n_2, 1, 0) → w_{10}
  29. If(u_8 ≟ n_1 ∨ u_8 ≟ n_2, 1, 0) → w_8
  30. If(u_6 ≟ n_1 ∨ u_6 ≟ n_2, 1, 0) → w_6
  31. If(u_5 ≟ n_1 ∨ u_5 ≟ n_2, 1, 0) → w_5
  32. If(u_4 ≟ n_1 ∨ u_4 ≟ n_2, 1, 0) → w_4
  33. If(u_3 ≟ n_1 ∨ u_3 ≟ n_2, 1, 0) → w_3
  34. If(u_7 ≟ n_1 ∨ u_7 ≟ n_2, 1, 0) → w_7
  35. If(u_9 ≟ n_1 ∨ u_9 ≟ n_2, 1, 0) → w_9
  36. If(u_{11} ≟ n_1 ∨ u_{11} ≟ n_2, 1, 0) → w_{11}
  37. If(u_{13} ≟ n_1 ∨ u_{13} ≟ n_2, 1, 0) → w_{13}
  38. If(u_{15} ≟ n_1 ∨ u_{15} ≟ n_2, 1, 0) → w_{15}
  39. If(u_{17} ≟ n_1 ∨ u_{17} ≟ n_2, 1, 0) → w_{17}
  40. If(u_{19} ≟ n_1 ∨ u_{19} ≟ n_2, 1, 0) → w_{19}
  41. Length(recordk) → s
  42. Intersect(xAxis, yAxis) → A
  43. Point(xAxis) → B
  44. Point(xAxis) → C
  45. Point(xAxis) → D
  46. Point(xAxis) → E
  47. Point(yAxis) → F
  48. Segment(F, A) → f
  49. Segment(B, G) → g
  50. Segment(H, C) → h
  51. Segment(I, D) → i
  52. Segment(E, J) → j
  53. Segment(A, E) → k
  54. Segment(F, J) → l
  55. Sequence(Segment[A + (0, i), E + (0, i)], i, 0, 10) → list1
  56. Sequence(Segment[K + (0, i), O + (0, i)], i, 0, 10) → list2
  57. Segment(P, K) → m
  58. Segment(L, G_1) → n
  59. Segment(M, H_1) → p
  60. Segment(I_1, N) → q
  61. Segment(O, J_1) → r
  62. Segment(J_1, P) → b
  63. Textfield(n_1) → InputBox11
  64. Textfield(n_2) → InputBox12
  65. Polygon(Q_1, Q_2, R, Q) → poly1, q_1, q_2, s_2, q_3
  66. Polygon(S, T, U, V) → poly2, s_1, t_1, u, v

AI Drawing Prompt Reference

Draw a coordinate system with x-axis and y-axis. Mark several points on the x-axis and one point on the y-axis. Draw a line segment from the point on the y-axis to the origin. The figure illustrates the relationship between probability and geometry, incorporating concepts like median lines, algebraic subtraction, and binomial distribution.
The prompt above was compiled from the original drawing commands and is for reference only.