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Sample Space for Four Coin Tosses

Sample Space for Four Coin Tosses
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2015-11-10 04:14
SequenceProbability & StatisticsSlider Animation
In collections CCSS Support Math II Unit 4
This example demonstrates all possible outcomes of tossing four coins, illustrating the concept of sample space in probability statistics. Using GeoGebra commands such as Sequence, Vector, and Random, it provides a visual representation of each possible outcome and its probability. Suitable for middle school and above students learning probability statistics.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a tree diagram for all possible outcomes of four coin tosses. Start by drawing four layers of branches, with each layer representing one coin toss and having two branches for heads and tails. Then label all possible outcomes at the end of each branch, such as HHHH, HHHT, ensuring all 8 possible outcomes are included.
The prompt above was compiled from the original drawing commands and is for reference only.