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Geometric Probability

Geometric Probability
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2014-11-07 01:09
FunctionProbability & StatisticsGeometric Construction
In collections Selected Examples
This example demonstrates the basic concept of geometric probability. By constructing geometric shapes, students can intuitively understand the relationship between probability and geometric shapes. Commands used include If, Segment, Polygon, and CountIf. Core mathematical concepts include geometric probability and conditional probability. Suitable for high school mathematics teaching, particularly in probability and statistics courses.

GeoGebra Commands & Parameters

  1. If(abs(A3 - B3) ≤ w, 1, 0) → C3
  2. If(abs(A4 - B4) ≤ w, 1, 0) → C4
  3. If(abs(A5 - B5) ≤ w, 1, 0) → C5
  4. If(abs(A6 - B6) ≤ w, 1, 0) → C6
  5. If(abs(A7 - B7) ≤ w, 1, 0) → C7
  6. If(abs(A8 - B8) ≤ w, 1, 0) → C8
  7. If(abs(A9 - B9) ≤ w, 1, 0) → C9
  8. If(abs(A10 - B10) ≤ w, 1, 0) → C10
  9. If(abs(A11 - B11) ≤ w, 1, 0) → C11
  10. If(abs(A12 - B12) ≤ w, 1, 0) → C12
  11. If(abs(A13 - B13) ≤ w, 1, 0) → C13
  12. If(abs(A14 - B14) ≤ w, 1, 0) → C14
  13. If(abs(A15 - B15) ≤ w, 1, 0) → C15
  14. If(abs(A16 - B16) ≤ w, 1, 0) → C16
  15. If(abs(A17 - B17) ≤ w, 1, 0) → C17
  16. If(abs(A18 - B18) ≤ w, 1, 0) → C18
  17. If(abs(A19 - B19) ≤ w, 1, 0) → C19
  18. If(abs(A20 - B20) ≤ w, 1, 0) → C20
  19. If(abs(A21 - B21) ≤ w, 1, 0) → C21
  20. If(abs(A22 - B22) ≤ w, 1, 0) → C22
  21. If(abs(A23 - B23) ≤ w, 1, 0) → C23
  22. If(abs(A24 - B24) ≤ w, 1, 0) → C24
  23. If(abs(A25 - B25) ≤ w, 1, 0) → C25
  24. If(abs(A26 - B26) ≤ w, 1, 0) → C26
  25. If(abs(A27 - B27) ≤ w, 1, 0) → C27
  26. If(abs(A28 - B28) ≤ w, 1, 0) → C28
  27. If(abs(A29 - B29) ≤ w, 1, 0) → C29
  28. If(abs(A30 - B30) ≤ w, 1, 0) → C30
  29. If(abs(A31 - B31) ≤ w, 1, 0) → C31
  30. If(abs(A32 - B32) ≤ w, 1, 0) → C32
  31. If(abs(A33 - B33) ≤ w, 1, 0) → C33
  32. If(abs(A34 - B34) ≤ w, 1, 0) → C34
  33. If(abs(A35 - B35) ≤ w, 1, 0) → C35
  34. If(abs(A36 - B36) ≤ w, 1, 0) → C36
  35. If(abs(A37 - B37) ≤ w, 1, 0) → C37
  36. If(abs(A38 - B38) ≤ w, 1, 0) → C38
  37. If(abs(A39 - B39) ≤ w, 1, 0) → C39
  38. If(abs(A40 - B40) ≤ w, 1, 0) → C40
  39. If(abs(A41 - B41) ≤ w, 1, 0) → C41
  40. If(abs(A42 - B42) ≤ w, 1, 0) → C42
  41. If(abs(A43 - B43) ≤ w, 1, 0) → C43
  42. If(abs(A44 - B44) ≤ w, 1, 0) → C44
  43. If(abs(A45 - B45) ≤ w, 1, 0) → C45
  44. If(abs(A46 - B46) ≤ w, 1, 0) → C46
  45. If(abs(A47 - B47) ≤ w, 1, 0) → C47
  46. If(abs(A48 - B48) ≤ w, 1, 0) → C48
  47. If(abs(A49 - B49) ≤ w, 1, 0) → C49
  48. If(abs(A50 - B50) ≤ w, 1, 0) → C50
  49. If(abs(A51 - B51) ≤ w, 1, 0) → C51
  50. If(abs(A52 - B52) ≤ w, 1, 0) → C52
  51. If(abs(A53 - B53) ≤ w, 1, 0) → C53
  52. If(abs(A54 - B54) ≤ w, 1, 0) → C54
  53. If(abs(A55 - B55) ≤ w, 1, 0) → C55
  54. If(abs(A56 - B56) ≤ w, 1, 0) → C56
  55. If(abs(A57 - B57) ≤ w, 1, 0) → C57
  56. If(abs(A58 - B58) ≤ w, 1, 0) → C58
  57. If(abs(A59 - B59) ≤ w, 1, 0) → C59
  58. If(abs(A60 - B60) ≤ w, 1, 0) → C60
  59. If(abs(A61 - B61) ≤ w, 1, 0) → C61
  60. If(abs(A62 - B62) ≤ w, 1, 0) → C62
  61. If(abs(A63 - B63) ≤ w, 1, 0) → C63
  62. If(abs(A64 - B64) ≤ w, 1, 0) → C64
  63. If(abs(A65 - B65) ≤ w, 1, 0) → C65
  64. If(abs(A66 - B66) ≤ w, 1, 0) → C66
  65. If(abs(A67 - B67) ≤ w, 1, 0) → C67
  66. If(abs(A68 - B68) ≤ w, 1, 0) → C68
  67. If(abs(A69 - B69) ≤ w, 1, 0) → C69
  68. If(abs(A70 - B70) ≤ w, 1, 0) → C70
  69. If(abs(A71 - B71) ≤ w, 1, 0) → C71
  70. If(abs(A72 - B72) ≤ w, 1, 0) → C72
  71. If(abs(A73 - B73) ≤ w, 1, 0) → C73
  72. If(abs(A74 - B74) ≤ w, 1, 0) → C74
  73. If(abs(A75 - B75) ≤ w, 1, 0) → C75
  74. If(abs(A76 - B76) ≤ w, 1, 0) → C76
  75. If(abs(A77 - B77) ≤ w, 1, 0) → C77
  76. If(abs(A78 - B78) ≤ w, 1, 0) → C78
  77. If(abs(A79 - B79) ≤ w, 1, 0) → C79
  78. If(abs(A80 - B80) ≤ w, 1, 0) → C80
  79. If(abs(A81 - B81) ≤ w, 1, 0) → C81
  80. If(abs(A82 - B82) ≤ w, 1, 0) → C82
  81. If(abs(A83 - B83) ≤ w, 1, 0) → C83
  82. If(abs(A84 - B84) ≤ w, 1, 0) → C84
  83. If(abs(A85 - B85) ≤ w, 1, 0) → C85
  84. If(abs(A86 - B86) ≤ w, 1, 0) → C86
  85. If(abs(A87 - B87) ≤ w, 1, 0) → C87
  86. If(abs(A88 - B88) ≤ w, 1, 0) → C88
  87. If(abs(A89 - B89) ≤ w, 1, 0) → C89
  88. If(abs(A90 - B90) ≤ w, 1, 0) → C90
  89. If(abs(A91 - B91) ≤ w, 1, 0) → C91
  90. If(abs(A92 - B92) ≤ w, 1, 0) → C92
  91. If(abs(A93 - B93) ≤ w, 1, 0) → C93
  92. If(abs(A94 - B94) ≤ w, 1, 0) → C94
  93. If(abs(A95 - B95) ≤ w, 1, 0) → C95
  94. If(abs(A96 - B96) ≤ w, 1, 0) → C96
  95. If(abs(A97 - B97) ≤ w, 1, 0) → C97
  96. If(abs(A98 - B98) ≤ w, 1, 0) → C98
  97. If(abs(A99 - B99) ≤ w, 1, 0) → C99
  98. If(abs(A100 - B100) ≤ w, 1, 0) → C100
  99. If(abs(A2 - B2) ≤ w, 1, 0) → C2
  100. If(abs(A101 - B101) ≤ w, 1, 0) → C101
  101. Segment(A, C) → f
  102. Polygon(A, B, C, D) → Vieleck1, a, b, c, d
  103. Polygon(A, I_4, K_4, C, L_4, J_4) → Vieleck2, e, g, h, i, j, k
  104. CountIf(x ≟ 1, C2:C101) → D2

AI Drawing Prompt Reference

Draw a square ABCD, then randomly select a point P inside the square. Next, draw a circle with P as the center and radius w. Finally, calculate the area of the overlapping part between the circle and the square, and compare it with the total area of the square to intuitively understand the concept of geometric probability.
The prompt above was compiled from the original drawing commands and is for reference only.