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比较实验概率与理论概率

比较实验概率与理论概率
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2018-07-07 02:42
函数解析几何概率统计
本范例演示如何通过实验概率与理论概率的比较，理解概率统计的基本概念。使用了Sequence, Polygon, Segment, Textfield, LaTeX, Translate, If等GeoGebra命令，适合高中数学教学。

GeoGebra 命令及参数

  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 绘图提示语参考

画一个包含多个水平线段和彩色多边形的统计图表，用于比较实验和理论概率。图表底部有三个不同宽度的水平条，分别代表不同的实验结果，条形上方有多个小矩形条，用于表示频数。图表左侧有垂直线段分隔不同区域，并包含文本标签，如“值”、“频率”、“点数”等，用于解释图表内容。
以上提示语为根据原始绘图命令整理而来，仅供参考。