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Experimental Probability Demo

Experimental Probability Demo
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2018-06-21 21:49
PolygonFunctionProbability & Statistics
This example demonstrates experimental probability calculation and visualization by simulating random events to show frequency distribution. Core math concepts include probability & statistics, polygons, random variables, function graphs, and integral calculus. GeoGebra commands used are Sequence, Polygon, Segment, Textfield, LaTeX, and If for construction. Suitable for high school probability statistics teaching and introductory mathematical modeling.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw an experimental probability demonstration diagram, including a table with horizontal lines above it, composed of multiple rectangles representing the results of each trial. Draw three vertical lines on the left side of the table, representing the number of trials, the number of times the event occurred, and the number of times the event did not occur. Above the table, draw an input box to prompt the user to enter the probability. Below the table, draw two text boxes, one for displaying the formula to calculate the experimental probability, and another for showing the user's answer.
The prompt above was compiled from the original drawing commands and is for reference only.