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实验概率演示

实验概率演示
几何画板及绘图内容加载中，请稍等……
2018-06-21 21:49
多边形函数概率统计
①本范例演示了实验概率的计算与可视化，通过模拟随机事件展示频率分布；②涉及核心数学概念包括概率统计、多边形、随机变量、函数图像及积分计算；③构造要点运用了 GeoGebra 命令 Sequence（数列）、Polygon（多边形）、Segment（线段）、Textfield（文本框）、LaTeX（公式渲染）、If（条件判断）；④适合高中阶段概率统计教学及数学建模入门学习。

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((((((((((("A\ " * object) * "\ is\ ") * action) * "\ ") * NumTrials) * "\ times.\ The\ following\ table\ summarizes\ the\ results.\\ Based\ on\ the\ data,\, what\ is\ the\ probability\ of\ ") * action2) * "\ ") * event) * "?")) → Instructions
  8. LaTeX("Type\ a\ number\ into\ the\ input\ box\\ before\ checking\ your\ answer.") → FeedbackNS
  9. LaTeX("Correct!") → FeedbackCorrect
  10. LaTeX("That\ is\ not\ correct.\\ Please\ try\ again.") → FeedbackWrong1
  11. LaTeX("\times") → Wrong
  12. LaTeX("\checkmark") → Right
  13. If(favoutcomes ≟ 1, "trial", "trials") → trials
  14. LaTeX("The\ experimental\ probability\ is") → Prob
  15. LaTeX((((((((((((((((((((((("There\ were\ " * NumTrials) * "\ ") * trials) * ".\\ ") * eventCap) * "\ ") * was) * "\ observed\ in\ ") * favoutcomes) * "\ ") * trials) * ".\\\ \\ Thus,\, the\ experimental\ probability\\ of\ ") * action2) * "\ ") * event) * "\ is\ \dfrac{") * favoutcomes) * "}{") * NumTrials) * "}") * or) * ".")) → FeedbackWrong
  16. Polygon(StartPoint + (TableW1, (-TableHeight)), StartPoint + (TableW1 + TableW2, (-TableHeight)), StartPoint + (TableW1 + TableW2, (-2 * TableHeight)), StartPoint + (TableW1, (-2 * TableHeight))) → Box1, i, j, k, l
  17. Polygon(StartPoint + (TableW1, (-2 * TableHeight)), StartPoint + (TableW1 + TableW2, (-2 * TableHeight)), StartPoint + (TableW1 + TableW2, (-3 * TableHeight)), StartPoint + (TableW1, (-3 * TableHeight))) → Box2, m, n, p, q
  18. Polygon(StartPoint + (TableW1, (-3 * TableHeight)), StartPoint + (TableW1 + TableW2, (-3 * TableHeight)), StartPoint + (TableW1 + TableW2, (-4 * TableHeight)), StartPoint + (TableW1, (-4 * TableHeight))) → Box3, r, s, t, a
  19. Polygon(StartPoint + (TableW1, (-4 * TableHeight)), StartPoint + (TableW1 + TableW2, (-4 * TableHeight)), StartPoint + (TableW1 + TableW2, (-5 * TableHeight)), StartPoint + (TableW1, (-5 * TableHeight))) → Box4, b, c, d, e
  20. Polygon(StartPoint + (TableW1, (-5 * TableHeight)), StartPoint + (TableW1 + TableW2, (-5 * TableHeight)), StartPoint + (TableW1 + TableW2, (-6 * TableHeight)), StartPoint + (TableW1, (-6 * TableHeight))) → Box5, f_1, g_1, h_1, i_1
  21. Polygon(StartPoint + (TableW1, (-6 * TableHeight)), StartPoint + (TableW1 + TableW2, (-6 * TableHeight)), StartPoint + (TableW1 + TableW2, (-7 * TableHeight)), StartPoint + (TableW1, (-7 * TableHeight))) → Box6, j_1, k_1, l_1, m_1
  22. LaTeX("\textbf{Instructions\text{:}}\ Enter\ the\ probability\ as\ a\ fraction\ in\ the\ input\ box.") → Instructions2

AI 绘图提示语参考

绘制一个实验概率演示图，包含一个表格，表格上方有水平线，表格由多个矩形组成，每个矩形代表一次试验的结果。在表格左侧绘制三条垂直线，分别代表试验次数、事件发生次数和事件未发生次数。在表格上方绘制一个输入框，提示用户输入概率。在表格下方绘制两个文本框，一个用于显示实验概率的计算公式，另一个用于显示用户输入的答案。
以上提示语为根据原始绘图命令整理而来，仅供参考。