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四枚硬币的投掷结果样本空间

四枚硬币的投掷结果样本空间
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2015-11-10 04:14
数列概率统计滑块动画
所属专题 CCSS Support Math II Unit 4
本范例演示了四枚硬币投掷的所有可能结果，展示了概率统计中的样本空间概念。通过使用GeoGebra命令如Sequence、Vector和Random，可以直观地展示每种可能的结果及其概率。适合初中及以上学生学习概率统计。

GeoGebra 命令及参数

  1. Segment((0, 0), (0, 1)) → i
  2. Segment(A_0, B_0) → Scaleline
  3. Sequence(Segment[A_0 + (i, 0), A_0 + (i, (-0.5))], i, 0, 10) → list1
  4. Sequence(Segment[A_0 + (i - 0.5, 0), A_0 + (i - 0.5, (-0.4))], i, 1, 10) → list2
  5. Sequence(Sequence[Segment[A_0 + ((0.5 * i) + (0.1 * j), 0), A_0 + ((0.5 * i) + (0.1 * j), (-0.3))], j, 1, 4], i, 0, 19) → list3
  6. Segment(D_0, (x(D_0), 0)) → j
  7. Vector(C_0, D_0) → u
  8. LaTeX("\text{Create a tree diagram.}") → Pg1C
  9. LaTeX("\text{Each coin has only two sides and therefore only two possible outcomes—heads \textcolor{#000099}{(H)} or tails \textcolor{#000099}{(T)}.}") → Pg1D_1
  10. LaTeX("\text{Make a tree diagram to list all the possible outcomes.}") → Pg1D
  11. LaTeX("\text{List the possible outcomes.}") → Pg1E
  12. LaTeX("\text{Follow the paths to find the possible outcomes.}") → Pg1F
  13. LaTeX("\text{Determine the sample space.}") → Pg1I
  14. LaTeX("\text{Determine the sample space.}") → Pg1I_5
  15. LaTeX("\text{Determine the sample space.}") → Pg1I_1
  16. LaTeX("\text{}") → WTK2
  17. LaTeX((("\text{Jenna tosses \textcolor{#000099}{" * Slider1) * "} coins into the air and records the result of the toss.What is the sample space for this experiment?}")) → Pg1A
  18. LaTeX((("\text{Number of times Coin tossed=" * Slider1) * "}")) → DKT1
  19. LaTeX("\text{\textcolor{#000099}{THHH},\textcolor{#000099}{THHT},\textcolor{#000099}{THTH},\textcolor{#000099}{THTT},\textcolor{#000099}{TTHH},\textcolor{#000099}{TTHT},\textcolor{#000099}{TTTH},\textcolor{#000099}{TTTT}\}.") → Pg2B_4
  20. LaTeX("\text{The possible outcomes are:\textcolor{#000099}{HHHHH},\textcolor{#000099}{HHHHT},\textcolor{#000099}{HHHTH},\textcolor{#000099}{HHHTT},\textcolor{#000099}{HHTHH},\textcolor{#000099}{HHTHT},\textcolor{#000099}{HHTTH},\textcolor{#000099}{HHTTT},\textcolor{#000099}{HTHHH},\textcolor{#000099}{HTHHT},}") → Pg1G_5
  21. LaTeX("\text{\textcolor{#000099}{HTHTH},\textcolor{#000099}{HTHTT},\textcolor{#000099}{HTTHH},\textcolor{#000099}{HTTHT},\textcolor{#000099}{HTTTH},\textcolor{#000099}{HTTTT},\textcolor{#000099}{THHHH},\textcolor{#000099}{THHHT},\textcolor{#000099}{THHTH},\textcolor{#000099}{THHTT},\textcolor{#000099}{THTHH},\textcolor{#000099}{THTHT},\textcolor{#000099}{THTTH}, }") → Pg1H_5
  22. LaTeX("\text{\textcolor{#000099}{THTTT},\textcolor{#000099}{TTHHH},\textcolor{#000099}{TTHHT},\textcolor{#000099}{TTHTH},\textcolor{#000099}{TTHTT},\textcolor{#000099}{TTTHH},\textcolor{#000099}{TTTHT},\textcolor{#000099}{TTTTH},and \textcolor{#000099}{TTTTT}.}") → Pg1H_1
  23. LaTeX("\text{The sample space is the set of all \textcolor{#000099}{32} possible outcomes:\{\textcolor{#000099}{HHHHH},\textcolor{#000099}{HHHHT},\textcolor{#000099}{HHHTH},\textcolor{#000099}{HHHTT},\textcolor{#000099}{HHTHH},\textcolor{#000099}{HHTHT},\textcolor{#000099}{HHTTH},}") → Pg2A_5
  24. LaTeX("\text{\textcolor{#000099}{HHTTT},\textcolor{#000099}{HTHHH},\textcolor{#000099}{HTHHT},\textcolor{#000099}{HTHTH},\textcolor{#000099}{HTHTT},\textcolor{#000099}{HTTHH},\textcolor{#000099}{HTTHT},\textcolor{#000099}{HTTTH},\textcolor{#000099}{HTTTT},\textcolor{#000099}{THHHH},\textcolor{#000099}{THHHT},\textcolor{#000099}{THHTH},\textcolor{#000099}{THHTT},}") → Pg2B_5
  25. LaTeX("\text{\textcolor{#000099}{THTHH},\textcolor{#000099}{THTHT},\textcolor{#000099}{THTTH},\textcolor{#000099}{THTTT},\textcolor{#000099}{TTHHH},\textcolor{#000099}{TTHHT},\textcolor{#000099}{TTHTH},\textcolor{#000099}{TTHTT},\textcolor{#000099}{TTTHH},\textcolor{#000099}{TTTHT},\textcolor{#000099}{TTTTH},\textcolor{#000099}{TTTTT}\}.}") → Pg2B_1
  26. LaTeX("\text{The possible outcomes are:\textcolor{#000099}{HHH},\textcolor{#000099}{HHT},\textcolor{#000099}{HTH},\textcolor{#000099}{HTT},\textcolor{#000099}{THH},\textcolor{#000099}{THT},\textcolor{#000099}{TTH},and \textcolor{#000099}{TTT}.}") → Pg1G_3
  27. LaTeX("\text{The sample space is the set of all \textcolor{#000099}{8} possible outcomes:\left\{ \textcolor{#000099}{HHH},\textcolor{#000099}{HHT},\textcolor{#000099}{HTH},\textcolor{#000099}{HTT},\textcolor{#000099}{THH},\textcolor{#000099}{THT},\textcolor{#000099}{TTH},\textcolor{#000099}{TTT} \right\}.}") → Pg2A_3
  28. LaTeX("\text{The possible outcomes are:\textcolor{#000099}{HHHH},\textcolor{#000099}{HHHT},\textcolor{#000099}{HHTH},\textcolor{#000099}{HHTT},\textcolor{#000099}{HTHH},\textcolor{#000099}{HTHT},\textcolor{#000099}{HTTH},\textcolor{#000099}{HTTT},\textcolor{#000099}{THHH},{\textcolor{#000099}{THHT},\textcolor{#000099}{THTH},\textcolor{#000099}{THTT},}") → Pg1G_4
  29. LaTeX("\text{\textcolor{#000099}{TTHH},\textcolor{#000099}{TTHT},\textcolor{#000099}{TTTH},and \textcolor{#000099}{TTTT}.}") → Pg1H_4
  30. LaTeX("\text{The sample space is the set of all \textcolor{#000099}{16} possible outcomes:\{\textcolor{#000099}{{HHHH},\textcolor{#000099}{HHHT},\textcolor{#000099}{HHTH},\textcolor{#000099}{HHTT},\textcolor{#000099}{HTHH},\textcolor{#000099}{HTHT},\textcolor{#000099}{HTTH},\textcolor{#000099}{HTTT},}") → Pg2A_4
  31. LaTeX("\text{ \mathbf{Sample\;space} the set of all possible outcomes of an experiment.}") → WTK1

AI 绘图提示语参考

画一个四次抛硬币的所有可能结果的树形图。首先画出四层分支，每层分支代表一次抛硬币，每层有两个分支，分别代表正面和反面。然后在每层分支的末端标注所有可能的结果，如HHHH, HHHT等，确保所有8种可能的结果都被列出。
以上提示语为根据原始绘图命令整理而来，仅供参考。