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Probability & Statistics: Lucky Wheel Probability Problems

Probability & Statistics: Lucky Wheel Probability Problems
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2024-06-19 17:24
Probability & StatisticsGeometric ConstructionGraphing
In collections Wahrscheinlichkeitsrechnung - Einführung
This example demonstrates probability calculations and decision-making analysis using a GeoGebra lucky wheel. It involves core math concepts like probability, comparing likelihoods, and statistical patterns. The construction summary utilizes commands/objects such as Circle, CircleSector, Point, Textfield, and Sequence. Suitable for 7th-8th grade students in probability & statistics education and activities.

GeoGebra Commands & Parameters

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {1, 3, 10, 3, 3, 8, 8, 9, 2, 7}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. Circle(MP, radius) → glücksrad1
  5. Circle(MP, radius + 0.3) → glücksrad2
  6. CircleSector(MP + (0, radius - 0.3), MP + (0, radius - 0.3) + (0.6 * (cos(80°), sin(80°))), MP + (0, radius - 0.3) + (0.6 * (cos(100°), sin(100°)))) → zeiger
  7. Sequence(MP + (radius * (cos(360° - k°), sin(360° - k°))), k, 0, 1079) → PGRList
  8. Point(PGRList) → PosGR0
  9. CircleSector(MP, PosGR1, PosGR8) → sek1
  10. CircleSector(MP, PosGR2, PosGR1) → sek2
  11. CircleSector(MP, PosGR3, PosGR2) → sek3
  12. CircleSector(MP, PosGR4, PosGR3) → sek4
  13. CircleSector(MP, PosGR5, PosGR4) → sek5
  14. CircleSector(MP, PosGR6, PosGR5) → sek6
  15. CircleSector(MP, PosGR7, PosGR6) → sek7
  16. CircleSector(MP, PosGR8, PosGR7) → sek8
  17. If(index1 < 360, 3, (-2.55 / (end1 - 360) * index1) + 3 + (2.55 * 360 / (end1 - 360))) → speed
  18. mean(Unique[RemoveUndefined[Sequence[IndexOf[true, SektorZeiger, k], k, 1, Length[SektorZeiger]]]]) → posSektor1
  19. PolyLine({PosSB, Corner[txt031, 1] + (0.5 * (Corner[txt031, 4] - Corner[txt031, 1])), Corner[txt031, 1], Corner[txt031, 2] + (0.2, 0), Corner[txt031, 3] + (0.2, 0.15), Corner[txt031, 4] + (0, 0.15), Corner[txt031, 1] + (0.5 * (Corner[txt031, 4] - Corner[txt031, 1])) + (0, 0.5), PosSB}) → sb03
  20. Point(PGRList) → PosGS0
  21. CircleSector(MP, PosGS1, PosGS7) → sek51
  22. CircleSector(MP, PosGS2, PosGS1) → sek52
  23. CircleSector(MP, PosGS3, PosGS2) → sek53
  24. CircleSector(MP, PosGS4, PosGS3) → sek54
  25. CircleSector(MP, PosGS5, PosGS4) → sek55
  26. CircleSector(MP, PosGS6, PosGS5) → sek56
  27. CircleSector(MP, PosGS7, PosGS6) → sek57
  28. Join({Sequence[MP + ((2 * radius / 3) * (cos(((-index2))° - (360° * (Sum[einteilung2, k] - einteilung2(k) / 2) / Sum[einteilung2])), sin(((-index2))° - (360° * (Sum[einteilung2, k] - einteilung2(k) / 2) / Sum[einteilung2])))), k, 1, Length[einteilung2]] + (-0.5, 0.48), Reverse[Sequence[StartStar + (k * (MP + ((-radius) - 1, 0) - StartStar)), k, 0, 1, 0.05]]}) → PosStarList
  29. Point(PosStarList) → PosStar
  30. Polygon(PosStar, PosStar + (1, 0), PosStar + (1, -0.96), PosStar + (0, -0.96)) → polyStar, posstar, f, g, h
  31. IndexOf(PosStar, PosStarList) → StarIndex
  32. PolyLine({PosSB, Corner[txt052, 1] + (0.5 * (Corner[txt052, 4] - Corner[txt052, 1])), Corner[txt052, 1], Corner[txt052, 2] + (0.2, 0), Corner[txt052, 3] + (0.2, 0.15), Corner[txt052, 4] + (0, 0.15), Corner[txt052, 1] + (0.5 * (Corner[txt052, 4] - Corner[txt052, 1])) + (0, 0.5), PosSB}) → sb052
  33. If(index2 < 360, 3, (-2.55 / (end2 - 360) * index2) + 3 + (2.55 * 360 / (end2 - 360))) → speed2
  34. PolyLine({PosSB, Corner[txt061, 1] + (0.5 * (Corner[txt061, 4] - Corner[txt061, 1])), Corner[txt061, 1], Corner[txt061, 2] + (0.2, 0), Corner[txt061, 3] + (0.2, 0.15), Corner[txt061, 4] + (0, 0.15), Corner[txt061, 1] + (0.5 * (Corner[txt061, 4] - Corner[txt061, 1])) + (0, 0.5), PosSB}) → sb06
  35. mean(Unique[RemoveUndefined[Sequence[IndexOf[true, SektorZeiger2, k], k, 1, Length[SektorZeiger2]]]]) → posSektor2
  36. If(step ≟ 3, gedreht1 ∧ posSektor1 ≟ 1 ∧ index1 ≟ end1, step ≟ 4, option41, step ≟ 5, StarIndex ≟ 2 ∧ showFB5, step ≟ 6, gedreht2 ∧ posSektor2 ≟ 2 ∧ index2 ≟ end2, true) → clickableBtnNext
  37. Remove(721…1080, Sequence[(k * 45), k, 1, 40]) → RandomList
  38. PolyLine({PosSB, Corner[txt011, 1] + (0.25 * (Corner[txt011, 4] - Corner[txt011, 1])), Corner[txt011, 1] + (0, -0.2), Corner[txt011, 2] + (0.2, -0.2), Corner[txt011, 3] + (0.2, 0.15), Corner[txt011, 4] + (0, 0.15), Corner[txt011, 1] + (0.25 * (Corner[txt011, 4] - Corner[txt011, 1])) + (0, 0.5), PosSB}) → sb01
  39. PolyLine({PosSB, Corner[txt021, 1] + (0.4 * (Corner[txt021, 4] - Corner[txt021, 1])), Corner[txt021, 1], Corner[txt021, 2] + (0.2, 0), Corner[txt021, 3] + (0.2, 0.15), Corner[txt021, 4] + (0, 0.15), Corner[txt021, 1] + (0.5 * (Corner[txt021, 4] - Corner[txt021, 1])) + (0, 0.5), PosSB}) → sb02
  40. PolyLine({PosSB, Corner[txt051, 1] + (0.4 * (Corner[txt051, 4] - Corner[txt051, 1])), Corner[txt051, 1], Corner[txt051, 2] + (0.2, 0), Corner[txt051, 3] + (0.2, 0.15), Corner[txt051, 4] + (0, 0.15), Corner[txt051, 1] + (0.5 * (Corner[txt051, 4] - Corner[txt051, 1])) + (0, 0.5), PosSB}) → sb05
  41. If(step ≟ 3, ¬drehen, true) → clickableBtnBack
  42. Join({Sequence[MP + ((2 * radius / 3) * (cos((-(index1°)) - (360° * (Sum[einteilung1, k] - einteilung1(k) / 2) / Sum[einteilung1])), sin((-(index1°)) - (360° * (Sum[einteilung1, k] - einteilung1(k) / 2) / Sum[einteilung1])))), k, 1, Length[einteilung1]] + (-0.5, 0.48), Reverse[Sequence[StartStar + (k * (MP + ((-radius) - 1, 0) - StartStar)), k, 0, 1, 0.05]]}) → PosStarList1
  43. Text("\textsf{\bold{Zieh mich!}}", MP + ((1.65 * radius) * (cos(((-index2))°), sin(((-index2))°))), false, true, 0, 0) → text8
  44. Text("\textsf{\bold{Zieh mich!}}", MP + ((1.35 * radius) * (cos((-(index1°))), sin((-(index1°))))), false, true, 0, 0) → text7
  45. Angle(MP + (1, 0), MP, PosGR0) → Angle03
  46. CircleArc(MP, PosArc, PosGR0) → arc03
  47. Segment(PosArc, PosArc + (0.01 * UnitVector[Tangent[PosArc, glücksrad1]])) → arrow03
  48. Angle(MP + (1, 0), MP, PosGS0) → Angle07
  49. CircleArc(MP, PosArc07, PosGS0) → arc07
  50. Segment(PosArc07, PosArc07 + (0.01 * UnitVector[Tangent[PosArc07, glücksrad1]])) → arrow07

AI Drawing Prompt Reference

This is a lucky wheel diagram with a central point surrounded by multiple sector regions. The sectors are separated by gaps, forming a circular structure. The diagram includes a larger main circle and a smaller inner circle, along with some star patterns. Text labels may appear between sectors. The overall layout is used for probability calculations and decision-making analysis, where the size and number of sectors represent different outcomes. The diagram is clear and helps visualize probability distributions.
The prompt above was compiled from the original drawing commands and is for reference only.