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GeoGebra概率事件示例

GeoGebra概率事件示例
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2015-11-10 04:19
概率统计几何作图函数图像
所属专题 CCSS Support Math II Unit 4
①本范例演示了从两个袋子中分别抽取球，并识别满足特定条件的所有可能结果；②涉及的核心数学概念为概率统计，特别是组合与事件概率的计算；③作图要点使用了GeoGebra命令If、LaTeX、对象Border、Gear、Book、P、Q、Striped0-3等，用于创建条件判断、文本显示和图形元素；④适合初中及以上学生，用于概率统计教学和事件分析。

GeoGebra 命令及参数

  1. If(Black ≟ 1 ∧ White ≟ 1 ∧ Gray ≟ 1, LaTeX["\text{Simon draws \textcolor{#000099}{1} marble from each bag shown.He hopes to draw \textcolor{#000099}{1} black marble,\textcolor{#000099}{1} white marble and \textcolor{#000099}{1} gray marble.}"]) → Pg1A1
  2. LaTeX("\text{Simon draws \textcolor{#000099}{1} marble from each bag shown.He hopes to draw \textcolor{#000099}{1} black marble,\textcolor{#000099}{1} striped marble and \textcolor{#000099}{1} gray marble.}") → Pg1A2
  3. LaTeX("\text{Simon draws \textcolor{#000099}{1} marble from each bag shown.He hopes to draw \textcolor{#000099}{1} striped marble,\textcolor{#000099}{1} white marble and \textcolor{#000099}{1} gray marble.}") → Pg1A3
  4. LaTeX("\text{Simon draws \textcolor{#000099}{1} marble from each bag shown.He hopes to draw \textcolor{#000099}{1} black marble,\textcolor{#000099}{1} white marble and \textcolor{#000099}{1}striped marble.}") → Pg1A4
  5. LaTeX("\text{Identify the outcomes that represent this event.}") → Pg1B
  6. LaTeX("\text{Identify the sample space.}") → Pg2A
  7. LaTeX("\text{Use a tree diagram to identify the sample space.}") → Pg2B
  8. LaTeX("\text{In the far left column of the diagram,list each marble possibility for the first bag:striped or black.In the}") → Pg2C
  9. LaTeX("\text{marble possibility for the third bag:striped or gray.Connect the branches as shown in the following diagram.}") → Pg2E
  10. LaTeX("\text{The sample space is all the possible outcomes.This can be determined by reading across each branch.}") → Pg3A
  11. LaTeX("\text{The possible outcomes are:}") → Pg3B
  12. LaTeX("\text{striped,white,striped}") → Pg3C1
  13. LaTeX("\text{black,white,striped}") → Pg3C2
  14. LaTeX("\text{striped,white,gray}") → Pg2D2
  15. LaTeX("\text{black,white,gray}") → Pg2D1
  16. LaTeX("\text{striped,striped,striped}") → Pg3D1
  17. LaTeX("\text{black,striped,striped}") → Pg3D2
  18. LaTeX("\text{striped,striped,gray}") → Pg3E2
  19. LaTeX("\text{black,striped,gray}") → Pg3E1
  20. LaTeX("\text{Identify all the outcomes in the event “drawing \textcolor{#000099}{1} gray marble and \textcolor{#000099}{2} striped marbles”.}") → Pg4A1
  21. LaTeX("\text{Identify all the outcomes in the event “drawing \textcolor{#000099}{1} gray marble,\textcolor{#000099}{1} white marble and \textcolor{#000099}{1} striped marbles”.}") → Pg4A4
  22. LaTeX("\text{Identify all the outcomes in the event “drawing \textcolor{#000099}{1} black marble and \textcolor{#000099}{2} striped marbles”.}") → Pg4A6
  23. LaTeX("\text{Identify all the outcomes in the event “drawing \textcolor{#000099}{1} white marble and \textcolor{#000099}{2} striped marbles”.}") → Pg4A7
  24. LaTeX("\text{Identify all the outcomes in the event “drawing \textcolor{#000099}{3} striped marbles”.}") → Pg4A8
  25. LaTeX("\text{The word “and” means the outcome must include \textcolor{#000099}{1} black marble and \textcolor{#000099}{2} striped marbles.}") → Pg4B6
  26. LaTeX("\text{The word “and” means the outcome must include \textcolor{#000099}{1} white marble and \textcolor{#000099}{2} striped marbles.}") → Pg4B7
  27. LaTeX("\text{It can be seen from the list of possible outcomes that there is only \textcolor{#000099}{1} outcome for which this is}") → Pg4B8
  28. If((Black ≠ 0) ∨ (White ≠ 0) ∨ (Gray ≠ 0), LaTeX["\text{It can be seen from the list of possible outcomes that there is only \textcolor{#000099}{1} outcome for which this is}"]) → Pg4C
  29. LaTeX("\text{possible:black,striped,striped.}") → Pg4D6
  30. LaTeX("\text{possible:striped,striped,striped.}") → Pg4D8
  31. LaTeX("\text{possible:black,white,gray.}") → Pg4D2
  32. LaTeX("\text{possible:striped,striped,gray.}") → Pg4D1
  33. LaTeX("\text{possible:striped,striped,white.}") → Pg4D7
  34. LaTeX("\text{possible:black,striped,gray.}") → Pg4D3
  35. LaTeX("\text{possible:striped,white,gray.}") → Pg4D4
  36. LaTeX("\text{possible:black,white,striped.}") → Pg4D5
  37. LaTeX((("\text{Black marble=" * Black) * "}")) → DKTblack
  38. LaTeX((("\text{White marble=" * White) * "}")) → DKTWhite
  39. LaTeX((("\text{Gray marble=" * Gray) * "}")) → DKTGray
  40. LaTeX((("\text{Striped marble=" * Total) * "}")) → DKTStriped
  41. LaTeX("\text{next column,list each marble possibility for the second bag:white or striped.In the next column,list each}") → Pg2D
  42. LaTeX("\text{that indicates how likely an event is to occur.}") → DKT2
  43. LaTeX("\text{Simon draws \textcolor{#000099}{1} marble from each bag shown.He hopes to draw \textcolor{#000099}{1} gray marble and \textcolor{#000099}{2} striped marbles.}") → Pg1A6
  44. LaTeX("\text{\mathbf{Probability} a number from \textcolor{#000099}0 to \textcolor{#000099}1 inclusive or a percent from \textcolor{#000099}{0%} to \textcolor{#000099}{100%} inclusive}") → WTK1
  45. LaTeX("\text{Simon draws \textcolor{#000099}{1} marble from each bag shown.He hopes to draw \textcolor{#000099}{1} black marble and \textcolor{#000099}{2} striped marbles.}") → Pg1A5
  46. LaTeX("\text{Simon draws \textcolor{#000099}{1} marble from each bag shown.He hopes to draw \textcolor{#000099}{1} white marble and \textcolor{#000099}{2} striped marbles.}") → Pg1A7
  47. LaTeX("\text{Simon draws \textcolor{#000099}{1} marble from each bag shown.He hopes to draw \textcolor{#000099}{3} striped marbles.}") → Pg1A8
  48. LaTeX("\text{The word “and” means the outcome must include \textcolor{#000099}{1} black marble,\textcolor{#000099}{1} white marble and \textcolor{#000099}{1} striped marble.}") → Pg4B5
  49. LaTeX("\text{The word “and” means the outcome must include \textcolor{#000099}{1} gray marble,\textcolor{#000099}{1} white marble and \textcolor{#000099}{1} striped marble.}") → Pg4B4
  50. LaTeX("\text{The word “and” means the outcome must include \textcolor{#000099}{1} gray marble,\textcolor{#000099}{1} black marble and \textcolor{#000099}{1} striped marble.}") → Pg4B3
  51. LaTeX("\text{The word “and” means the outcome must include \textcolor{#000099}{1} gray marble,\textcolor{#000099}{1} black marble and \textcolor{#000099}{1} white marble.}") → Pg4B2
  52. LaTeX("\text{Identify all the outcomes in the event “drawing \textcolor{#000099}{1} black marble,\textcolor{#000099}{1} white marble and \textcolor{#000099}{1} striped marble”.}") → Pg4A5
  53. LaTeX("\text{Identify all the outcomes in the event “drawing \textcolor{#000099}{1} gray marble,\textcolor{#000099}{1} striped marble and \textcolor{#000099}{1} black marble”.}") → Pg4A3
  54. LaTeX("\text{Identify all the outcomes in the event “drawing \textcolor{#000099}{1} gray marble,\textcolor{#000099}{1} white marble and \textcolor{#000099}{1} black marble”.}") → Pg4A2
  55. LaTeX("\text{The word “and” means the outcome must include \textcolor{#000099}{1} gray marble and \textcolor{#000099}{2} striped marbles.}") → Pg4B1

AI 绘图提示语参考

画两个袋子，每个袋子里有不同颜色的球，包括黑色、白色、灰色和条纹球。模拟Simon从每个袋子里各抽取一个球，希望抽到1个黑色球、1个白色球和1个灰色球。用文字说明这个事件，并列出所有可能的结果。接着，画一个树状图来表示所有可能的结果，包括每个球的可能组合。最后，找出所有包含1个灰色球和2个条纹球的结果。
以上提示语为根据原始绘图命令整理而来，仅供参考。