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Banach's Match Problem Simulation

Banach's Match Problem Simulation
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2016-06-09 01:05
SequenceProbability & StatisticsSlider Animation
In collections Statistics Simulations Statistics Simulations
This example demonstrates Banach's match problem, a probability and statistics problem involving the random selection of matches from a matchbox. Using GeoGebra commands such as Sequence and Shuffle, it simulates the process of randomly drawing matches from a box. The example illustrates how to use random number generation and statistical analysis to understand probability distributions. Suitable for high school probability and statistics courses.

GeoGebra Commands & Parameters

  1. Sequence(1, n, 1, 25) → left
  2. Sequence(0, n, 1, 25) → right
  3. Join({left, right}) → list1
  4. Shuffle(list1) → list2
  5. If(C2 ≟ 0, 0, If[B3 ≟ B2, 1, 0]) → C3
  6. If(C3 ≟ 0, 0, If[B4 ≟ B3, 1, 0]) → C4
  7. If(C4 ≟ 0, 0, If[B5 ≟ B4, 1, 0]) → C5
  8. If(C5 ≟ 0, 0, If[B6 ≟ B5, 1, 0]) → C6
  9. If(C6 ≟ 0, 0, If[B7 ≟ B6, 1, 0]) → C7
  10. If(C7 ≟ 0, 0, If[B8 ≟ B7, 1, 0]) → C8
  11. If(C8 ≟ 0, 0, If[B9 ≟ B8, 1, 0]) → C9
  12. If(C9 ≟ 0, 0, If[B10 ≟ B9, 1, 0]) → C10
  13. If(C10 ≟ 0, 0, If[B11 ≟ B10, 1, 0]) → C11
  14. If(C11 ≟ 0, 0, If[B12 ≟ B11, 1, 0]) → C12
  15. If(C12 ≟ 0, 0, If[B13 ≟ B12, 1, 0]) → C13
  16. If(C13 ≟ 0, 0, If[B14 ≟ B13, 1, 0]) → C14
  17. If(C14 ≟ 0, 0, If[B15 ≟ B14, 1, 0]) → C15
  18. If(C15 ≟ 0, 0, If[B16 ≟ B15, 1, 0]) → C16
  19. If(C16 ≟ 0, 0, If[B17 ≟ B16, 1, 0]) → C17
  20. If(C17 ≟ 0, 0, If[B18 ≟ B17, 1, 0]) → C18
  21. If(C18 ≟ 0, 0, If[B19 ≟ B18, 1, 0]) → C19
  22. If(C19 ≟ 0, 0, If[B20 ≟ B19, 1, 0]) → C20
  23. If(C20 ≟ 0, 0, If[B21 ≟ B20, 1, 0]) → C21
  24. If(C21 ≟ 0, 0, If[B22 ≟ B21, 1, 0]) → C22
  25. If(C22 ≟ 0, 0, If[B23 ≟ B22, 1, 0]) → C23
  26. If(C23 ≟ 0, 0, If[B24 ≟ B23, 1, 0]) → C24
  27. If(C24 ≟ 0, 0, If[B25 ≟ B24, 1, 0]) → C25
  28. If(C25 ≟ 0, 0, If[B26 ≟ B25, 1, 0]) → C26
  29. If(C26 ≟ 0, 0, If[B27 ≟ B26, 1, 0]) → C27
  30. If(C27 ≟ 0, 0, If[B28 ≟ B27, 1, 0]) → C28
  31. If(C28 ≟ 0, 0, If[B29 ≟ B28, 1, 0]) → C29
  32. If(C29 ≟ 0, 0, If[B30 ≟ B29, 1, 0]) → C30
  33. If(C30 ≟ 0, 0, If[B31 ≟ B30, 1, 0]) → C31
  34. If(C31 ≟ 0, 0, If[B32 ≟ B31, 1, 0]) → C32
  35. If(C32 ≟ 0, 0, If[B33 ≟ B32, 1, 0]) → C33
  36. If(C33 ≟ 0, 0, If[B34 ≟ B33, 1, 0]) → C34
  37. If(C34 ≟ 0, 0, If[B35 ≟ B34, 1, 0]) → C35
  38. If(C35 ≟ 0, 0, If[B36 ≟ B35, 1, 0]) → C36
  39. If(C36 ≟ 0, 0, If[B37 ≟ B36, 1, 0]) → C37
  40. If(C37 ≟ 0, 0, If[B38 ≟ B37, 1, 0]) → C38
  41. If(C38 ≟ 0, 0, If[B39 ≟ B38, 1, 0]) → C39
  42. If(C39 ≟ 0, 0, If[B40 ≟ B39, 1, 0]) → C40
  43. If(C40 ≟ 0, 0, If[B41 ≟ B40, 1, 0]) → C41
  44. If(C41 ≟ 0, 0, If[B42 ≟ B41, 1, 0]) → C42
  45. If(C42 ≟ 0, 0, If[B43 ≟ B42, 1, 0]) → C43
  46. If(C43 ≟ 0, 0, If[B44 ≟ B43, 1, 0]) → C44
  47. If(C44 ≟ 0, 0, If[B45 ≟ B44, 1, 0]) → C45
  48. If(C45 ≟ 0, 0, If[B46 ≟ B45, 1, 0]) → C46
  49. If(C46 ≟ 0, 0, If[B47 ≟ B46, 1, 0]) → C47
  50. If(C47 ≟ 0, 0, If[B48 ≟ B47, 1, 0]) → C48
  51. If(C48 ≟ 0, 0, If[B49 ≟ B48, 1, 0]) → C49
  52. If(C49 ≟ 0, 0, If[B50 ≟ B49, 1, 0]) → C50
  53. If(C50 ≟ 0, 0, If[B51 ≟ B50, 1, 0]) → C51
  54. Sum(C2:C51) → D2
  55. CountIf(x > 0, data) → a
  56. DotPlot(data, false, 0.2) → list3