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Comparing Experimental and Theoretical Probability

Comparing Experimental and Theoretical Probability
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2018-07-07 02:42
FunctionCoordinate GeometryProbability & Statistics
This example demonstrates the comparison between experimental and theoretical probability to understand basic concepts of probability and statistics. It uses commands like Sequence, Polygon, Segment, Textfield, LaTeX, Translate, If, etc., suitable for high school math education.

GeoGebra Commands & Parameters

  1. Sequence(Segment[StartPoint - (i * (0, TableHeight)), StartPoint + (TableW1 + TableW2, 0) - (i * (0, TableHeight))], i, 0, NumRows) → HorizontalLines
  2. Polygon(StartPoint, StartPoint + (TableW1 + TableW2, 0), StartPoint + (TableW1 + TableW2, (-TableHeight)), StartPoint + (0, (-TableHeight))) → ShadedTop, startpoint, f, g, h
  3. Segment(StartPoint, StartPoint - (0, (NumRows * TableHeight))) → LeftSegment
  4. Segment(StartPoint + (TableW1, 0), StartPoint + (TableW1, ((-NumRows) * TableHeight))) → MidSegment
  5. Segment(StartPoint + (TableW1 + TableW2, 0), StartPoint + (TableW1 + TableW2, ((-NumRows) * TableHeight))) → RightSegment
  6. Textfield(StudentAns) → StudentAnswer
  7. LaTeX("Type\ a\ number\ into\ the\ input\ box\\ before\ checking\ your\ answer.") → FeedbackNS
  8. LaTeX("\times") → Wrong
  9. LaTeX("\checkmark") → Right
  10. LaTeX("Value") → Value
  11. LaTeX("Frequency") → Frequency
  12. LaTeX("Tally") → Tally
  13. Segment(StartPoint + (TableW1 + TableW3, 0), StartPoint + (TableW1 + TableW3, ((-NumRows) * TableHeight))) → Mid2Segment
  14. Segment(StartPoint + (TableW1 + (2 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (2 * tallydist), (-2 * TableHeight) + tallyheight)) → T11
  15. Segment(StartPoint + (TableW1 + (3 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (3 * tallydist), (-2 * TableHeight) + tallyheight)) → T12
  16. Segment(StartPoint + (TableW1 + (4 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (4 * tallydist), (-2 * TableHeight) + tallyheight)) → T13
  17. Segment(StartPoint + (TableW1 + (5 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (5 * tallydist), (-2 * TableHeight) + tallyheight)) → T14
  18. Segment(StartPoint + (TableW1 + (7 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (7 * tallydist), (-2 * TableHeight) + tallyheight)) → T16
  19. Segment(StartPoint + (TableW1 + (8 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (8 * tallydist), (-2 * TableHeight) + tallyheight)) → T17
  20. Segment(StartPoint + (TableW1 + (9 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (9 * tallydist), (-2 * TableHeight) + tallyheight)) → T18
  21. Segment(StartPoint + (TableW1 + (10 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (10 * tallydist), (-2 * TableHeight) + tallyheight)) → T19
  22. Segment(StartPoint + (TableW1 + (12 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (12 * tallydist), (-2 * TableHeight) + tallyheight)) → T111
  23. Segment(StartPoint + (TableW1 + (13 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (13 * tallydist), (-2 * TableHeight) + tallyheight)) → T112
  24. Segment(StartPoint + (TableW1 + (14 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (14 * tallydist), (-2 * TableHeight) + tallyheight)) → T113
  25. Segment(StartPoint + (TableW1 + (15 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (15 * tallydist), (-2 * TableHeight) + tallyheight)) → T114
  26. Segment(StartPoint + (TableW1 + (17 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (17 * tallydist), (-2 * TableHeight) + tallyheight)) → T116
  27. Segment(StartPoint + (TableW1 + (18 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (18 * tallydist), (-2 * TableHeight) + tallyheight)) → T117
  28. Segment(StartPoint + (TableW1 + (19 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (19 * tallydist), (-2 * TableHeight) + tallyheight)) → T118
  29. Segment(StartPoint + (TableW1 + (20 * tallydist), (-TableHeight) - tallyheight), StartPoint + (TableW1 + (20 * tallydist), (-2 * TableHeight) + tallyheight)) → T119
  30. Segment(StartPoint + (TableW1 + (1.5 * tallydist), (-3 / 2 * TableHeight)), StartPoint + (TableW1 + (5.5 * tallydist), (-3 / 2 * TableHeight))) → T15
  31. Segment(StartPoint + (TableW1 + (6.5 * tallydist), (-3 / 2 * TableHeight)), StartPoint + (TableW1 + (10.5 * tallydist), (-3 / 2 * TableHeight))) → T110
  32. Segment(StartPoint + (TableW1 + (11.5 * tallydist), (-3 / 2 * TableHeight)), StartPoint + (TableW1 + (15.5 * tallydist), (-3 / 2 * TableHeight))) → T115
  33. Segment(StartPoint + (TableW1 + (16.5 * tallydist), (-3 / 2 * TableHeight)), StartPoint + (TableW1 + (20.5 * tallydist), (-3 / 2 * TableHeight))) → T120
  34. Translate(T11, (0, (-TableHeight))) → T21
  35. Translate(T12, (0, (-TableHeight))) → T22
  36. Translate(T13, (0, (-TableHeight))) → T23
  37. Translate(T14, (0, (-TableHeight))) → T24
  38. Translate(T15, (0, (-TableHeight))) → T25
  39. Translate(T16, (0, (-TableHeight))) → T26
  40. Translate(T17, (0, (-TableHeight))) → T27
  41. Translate(T18, (0, (-TableHeight))) → T28
  42. Translate(T19, (0, (-TableHeight))) → T29
  43. Translate(T110, (0, (-TableHeight))) → T210
  44. Translate(T111, (0, (-TableHeight))) → T211
  45. Translate(T112, (0, (-TableHeight))) → T212
  46. Translate(T113, (0, (-TableHeight))) → T213
  47. Translate(T114, (0, (-TableHeight))) → T214
  48. Translate(T115, (0, (-TableHeight))) → T215
  49. Translate(T116, (0, (-TableHeight))) → T216
  50. Translate(T117, (0, (-TableHeight))) → T217
  51. Translate(T118, (0, (-TableHeight))) → T218
  52. Translate(T119, (0, (-TableHeight))) → T219
  53. Translate(T120, (0, (-TableHeight))) → T220
  54. Translate(T21, (0, (-TableHeight))) → T31
  55. Translate(T22, (0, (-TableHeight))) → T32
  56. Translate(T23, (0, (-TableHeight))) → T33
  57. Translate(T24, (0, (-TableHeight))) → T34
  58. Translate(T25, (0, (-TableHeight))) → T35
  59. Translate(T26, (0, (-TableHeight))) → T36
  60. Translate(T27, (0, (-TableHeight))) → T37
  61. Translate(T28, (0, (-TableHeight))) → T38
  62. Translate(T29, (0, (-TableHeight))) → T39
  63. Translate(T210, (0, (-TableHeight))) → T310
  64. Translate(T211, (0, (-TableHeight))) → T311
  65. Translate(T212, (0, (-TableHeight))) → T312
  66. Translate(T213, (0, (-TableHeight))) → T313
  67. Translate(T214, (0, (-TableHeight))) → T314
  68. Translate(T215, (0, (-TableHeight))) → T315
  69. Translate(T216, (0, (-TableHeight))) → T316
  70. Translate(T217, (0, (-TableHeight))) → T317
  71. Translate(T218, (0, (-TableHeight))) → T318
  72. Translate(T219, (0, (-TableHeight))) → T319
  73. Translate(T220, (0, (-TableHeight))) → T320
  74. Translate(T31, (0, (-TableHeight))) → T41
  75. Translate(T32, (0, (-TableHeight))) → T42
  76. Translate(T33, (0, (-TableHeight))) → T43
  77. Translate(T34, (0, (-TableHeight))) → T44
  78. Translate(T35, (0, (-TableHeight))) → T45
  79. Translate(T36, (0, (-TableHeight))) → T46
  80. Translate(T37, (0, (-TableHeight))) → T47
  81. Translate(T38, (0, (-TableHeight))) → T48
  82. Translate(T39, (0, (-TableHeight))) → T49
  83. Translate(T310, (0, (-TableHeight))) → T410
  84. Translate(T311, (0, (-TableHeight))) → T411
  85. Translate(T312, (0, (-TableHeight))) → T412
  86. Translate(T313, (0, (-TableHeight))) → T413
  87. Translate(T314, (0, (-TableHeight))) → T414
  88. Translate(T315, (0, (-TableHeight))) → T415
  89. Translate(T316, (0, (-TableHeight))) → T416
  90. Translate(T317, (0, (-TableHeight))) → T417
  91. Translate(T318, (0, (-TableHeight))) → T418
  92. Translate(T319, (0, (-TableHeight))) → T419
  93. Translate(T320, (0, (-TableHeight))) → T420
  94. Translate(T41, (0, (-TableHeight))) → T51
  95. Translate(T42, (0, (-TableHeight))) → T52
  96. Translate(T43, (0, (-TableHeight))) → T53
  97. Translate(T44, (0, (-TableHeight))) → T54
  98. Translate(T45, (0, (-TableHeight))) → T55
  99. Translate(T46, (0, (-TableHeight))) → T56
  100. Translate(T47, (0, (-TableHeight))) → T57
  101. Translate(T48, (0, (-TableHeight))) → T58
  102. Translate(T49, (0, (-TableHeight))) → T59
  103. Translate(T410, (0, (-TableHeight))) → T510
  104. Translate(T411, (0, (-TableHeight))) → T511
  105. Translate(T412, (0, (-TableHeight))) → T512
  106. Translate(T413, (0, (-TableHeight))) → T513
  107. Translate(T414, (0, (-TableHeight))) → T514
  108. Translate(T415, (0, (-TableHeight))) → T515
  109. Translate(T416, (0, (-TableHeight))) → T516
  110. Translate(T417, (0, (-TableHeight))) → T517
  111. Translate(T418, (0, (-TableHeight))) → T518
  112. Translate(T419, (0, (-TableHeight))) → T519
  113. Translate(T420, (0, (-TableHeight))) → T520
  114. Translate(T51, (0, (-TableHeight))) → T61
  115. Translate(T52, (0, (-TableHeight))) → T62
  116. Translate(T53, (0, (-TableHeight))) → T63
  117. Translate(T54, (0, (-TableHeight))) → T64
  118. Translate(T55, (0, (-TableHeight))) → T65
  119. Translate(T56, (0, (-TableHeight))) → T66
  120. Translate(T57, (0, (-TableHeight))) → T67
  121. Translate(T58, (0, (-TableHeight))) → T68
  122. Translate(T59, (0, (-TableHeight))) → T69
  123. Translate(T510, (0, (-TableHeight))) → T610
  124. Translate(T511, (0, (-TableHeight))) → T611
  125. Translate(T512, (0, (-TableHeight))) → T612
  126. Translate(T513, (0, (-TableHeight))) → T613
  127. Translate(T514, (0, (-TableHeight))) → T614
  128. Translate(T515, (0, (-TableHeight))) → T615
  129. Translate(T516, (0, (-TableHeight))) → T616
  130. Translate(T517, (0, (-TableHeight))) → T617
  131. Translate(T518, (0, (-TableHeight))) → T618
  132. Translate(T519, (0, (-TableHeight))) → T619
  133. Translate(T520, (0, (-TableHeight))) → T620
  134. LaTeX("The\ experiment\ is\ over.\\ Now\ use\ the\ data\ to\ find\ the\ probability.") → ExperimentOverText
  135. If(favoutcomes ≟ 1, "trial", "trials") → trials
  136. LaTeX("The\ experimental\ probability\ is") → Prob
  137. LaTeX((((((((((((((((((("You\ performed\ " * NumTried) * "\ trials.\\ ") * eventCap) * "\ occurred\ in\ ") * favoutcomes) * "\ ") * trials) * ".\\\ \\ According\ to\ this\ experiment,\, the\ probability\\ of\ ") * action2) * "\ ") * event) * "\ is\ \dfrac{") * favoutcomes) * "}{") * NumTried) * "}") * or) * ".")) → FeedbackWrong
  138. LaTeX("The\ theoretical\ probability\ is") → TheoreticalPro
  139. Textfield(StudentAns2) → StudentAnsSecond
  140. LaTeX("\times") → Wrong2
  141. LaTeX("\checkmark") → Correct2
  142. LaTeX("\textbf{Instructions\text{:}}\ Enter\ the\ probability\ in\ the\ input\ box.") → TheoInstructions2
  143. LaTeX(action3 + ((((("\ the\ " * object) * "\ at\ least\ ") * MinTimes) * "\ times\\ before\ ending\ the\ experiment."))) → FBNotEnoughTrials
  144. LaTeX("Correct!") → FeedbackCorrect
  145. LaTeX("End\ the\ experiment\ before\ checking\ your\ work.") → FBEndExperiment
  146. LaTeX((("That\ is\ not\ correct.\\ You\ performed\ " * NumTried) * "\ trials.\, Count\ the\ number\ of\\ trials\ that\ had\ favourable\ outcomes\ and\ try\ again.")) → FeedbackWrong1
  147. LaTeX((((((((("A\ " * object) * "\ is\ ") * action) * ".\ What\ is\ the\ theoretical\ probability\ of\ ") * action2) * "\ ") * event) * "?")) → TheoInstructions
  148. LaTeX((("\textbf{Instructions\text{:}}\ Press\ the\ \textbf{Run\ a\ Trial}\ button\ to\ " * BDlowercase) * ".\\ End\ the\ experiment\ and\ then\ enter\ the\ experimental\ probability\ into\ the\ input\ box.")) → Instructions2
  149. LaTeX("Part\ 1") → Part1
  150. LaTeX("Part\ 2") → Part2
  151. LaTeX(("Total\ number\ of\ trials\text{:}\ " * NumTried)) → TotalTrials
  152. LaTeX(("Total\ number\ of\ trials\text{:}\ " * NumTried)) → TotalTrials2
  153. LaTeX((((((((((((((((("Incorrect.\\ There\ are\ " * Tposoutcomes) * "\ outcomes\ and\ ") * Tfavoutcomes) * "\ of\ those\ outcomes\ ") * Tis) * "\ favourable.\\ Therefore\ the\ theoretical\ probability\ of\ ") * action2) * "\ ") * event) * "\ is\ \dfrac{") * Tfavoutcomes) * "}{") * Tposoutcomes) * "}") * Tor) * ".")) → TheoFeedback
  154. LaTeX((((((((((action3 * "\ the\ ") * object) * "\ at\ least\ ") * MinTimes) * "\ times.\ The\ table\ below\ will\ summarize\ the\ results.\\ Use\ the\ data\ you\ collect\ to\ find\ the\ experimental\ probability\ of\ \textbf{") * action2) * " \ ") * event) * "}.")) → Instructions

AI Drawing Prompt Reference

Create a statistical chart comparing experimental and theoretical probability, featuring multiple horizontal line segments and colored polygons. The chart includes three horizontal bars at the bottom with varying widths, representing different experimental outcomes, and small rectangular bars above them to indicate frequencies. Vertical line segments separate different sections, with text labels like 'Value', 'Frequency', 'Tally' to explain the content.
The prompt above was compiled from the original drawing commands and is for reference only.