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Comparing Probability Outcomes With and Without Replacement

Comparing Probability Outcomes With and Without Replacement
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2024-02-15 03:37
Probability & StatisticsGeometric ConstructionGraphing
This example demonstrates how compound probabilities differ with or without replacement using a tree diagram. It involves core math concepts like probability calculation, compound events, and conditional probability. The construction utilizes GeoGebra commands such as Corner, Sequence, Flatten, Zip, Dilate, Translate, Polygon, If, etc., to build the tree diagram and show different probability paths under various conditions. Suitable for students in grades 6-8 learning to determine the probability of compound events with and without replacement.

GeoGebra Commands & Parameters

  1. Corner(5) → AppSize
  2. Sequence(((ii * 5.25), 2), ii, 0, 2) → IniPoints
  3. Flatten(Zip[{Segment[PP, PP - (sep1, 1.5)], Segment[PP, PP - (0, 1.5)], Segment[PP, PP - ((-sep1), 1.5)]}, PP, IniPoints]) → segsAbove
  4. Zip(Vertex[SS, 2], SS, segsAbove) → MidPoints
  5. Flatten(Zip[{Segment[PP, PP - (sep2, 1.5)], Segment[PP, PP - (0, 1.5)], Segment[PP, PP - ((-sep2), 1.5)]}, PP, MidPoints]) → segsBelow
  6. Zip(Vertex[SS, 2], SS, segsBelow) → EndPoints
  7. Flatten(Zip[{Segment[PP, PP - (sep1, 1.5)], Segment[PP, PP - ((-sep1), 1.5)]}, PP, IniPoints]) → segsAboveNR
  8. Zip(Vertex[SS, 2], SS, segsAboveNR) → MidPointsNR
  9. Zip(Segment[PP, PP - (0, 1.5)], PP, MidPointsNR) → segsBelowNR
  10. Zip(Vertex[SS, 2], SS, segsBelowNR) → EndPointsNR
  11. Zip({PP - (sep2 / 2, sep2 / 2), PP - (((-sep2)) / 2, sep2 / 2)}, PP, EndPoints) → m1
  12. Dilate(pic1, 0.35, A) → pic1small
  13. Translate(pic1small, Vector[A, EndPoints(1)]) → pic1B11
  14. Translate(pic1small, Vector[A, EndPoints(4)]) → pic1B12
  15. Translate(pic1small, Vector[A, EndPoints(7)]) → pic1B13
  16. Translate(pic1small, Vector[A, EndPoints(10)]) → pic1B21
  17. Translate(pic1small, Vector[A, EndPoints(13)]) → pic1B22
  18. Translate(pic1small, Vector[A, EndPoints(16)]) → pic1B23
  19. Translate(pic1small, Vector[A, EndPoints(19)]) → pic1B31
  20. Translate(pic1small, Vector[A, EndPoints(22)]) → pic1B32
  21. Translate(pic1small, Vector[A, EndPoints(25)]) → pic1B33
  22. Dilate(pic2, 0.35, B) → pic2small
  23. Translate(pic2small, Vector[B, EndPoints(2)]) → pic2B11
  24. Translate(pic2small, Vector[B, EndPoints(5)]) → pic2B12
  25. Translate(pic2small, Vector[B, EndPoints(8)]) → pic2B13
  26. Translate(pic2small, Vector[B, EndPoints(11)]) → pic2B21
  27. Translate(pic2small, Vector[B, EndPoints(14)]) → pic2B22
  28. Translate(pic2small, Vector[B, EndPoints(17)]) → pic2B23
  29. Translate(pic2small, Vector[B, EndPoints(20)]) → pic2B31
  30. Translate(pic2small, Vector[B, EndPoints(23)]) → pic2B32
  31. Translate(pic2small, Vector[B, EndPoints(26)]) → pic2B33
  32. Dilate(pic3, 0.35, C) → pic3small
  33. Translate(pic3small, Vector[C, EndPoints(3)]) → pic3B11
  34. Translate(pic3small, Vector[C, EndPoints(6)]) → pic3B12
  35. Translate(pic3small, Vector[C, EndPoints(9)]) → pic3B13
  36. Translate(pic3small, Vector[C, EndPoints(12)]) → pic3B21
  37. Translate(pic3small, Vector[C, EndPoints(15)]) → pic3B22
  38. Translate(pic3small, Vector[C, EndPoints(18)]) → pic3B23
  39. Translate(pic3small, Vector[C, EndPoints(21)]) → pic3B31
  40. Translate(pic3small, Vector[C, EndPoints(24)]) → pic3B32
  41. Translate(pic3small, Vector[C, EndPoints(27)]) → pic3B33
  42. Translate(pic3small, Vector[C, MidPoints(3)]) → pic3M1
  43. Translate(pic3small, Vector[C, MidPoints(6)]) → pic3M2
  44. Translate(pic3small, Vector[C, MidPoints(9)]) → pic3M3
  45. Translate(pic2small, Vector[B, MidPoints(2)]) → pic2M1
  46. Translate(pic2small, Vector[B, MidPoints(5)]) → pic2M2
  47. Translate(pic2small, Vector[B, MidPoints(8)]) → pic2M3
  48. Translate(pic1small, Vector[A, MidPoints(1)]) → pic1M1
  49. Translate(pic1small, Vector[A, MidPoints(4)]) → pic1M2
  50. Translate(pic1small, Vector[A, MidPoints(7)]) → pic1M3
  51. Translate(pic1small, Vector[A, IniPoints(1)]) → pic1T
  52. Translate(pic2small, Vector[B, IniPoints(2)]) → pic2T
  53. Translate(pic3small, Vector[C, IniPoints(3)]) → pic3T
  54. Zip(Circle[PP, 0.35], PP, IniPoints) → l1
  55. Zip(Circle[PP, 0.35], PP, If[repYESNO, MidPoints, MidPointsNR]) → l2
  56. Zip(Circle[PP, 0.35], PP, If[repYESNO, EndPoints, EndPointsNR]) → l3
  57. Translate(pic1small, Vector[A, MidPointsNR(3)]) → pic1M2NR
  58. Translate(pic1small, Vector[A, MidPointsNR(5)]) → pic1M3NR
  59. Translate(pic2small, Vector[B, MidPointsNR(1)]) → pic2M1NR
  60. Translate(pic2small, Vector[B, MidPointsNR(6)]) → pic2M3NR
  61. Translate(pic3small, Vector[C, MidPointsNR(2)]) → pic3M1NR
  62. Translate(pic3small, Vector[C, MidPointsNR(4)]) → pic3M2NR
  63. Translate(pic3small, Vector[C, EndPointsNR(1)]) → pic3B11NR
  64. Translate(pic3small, Vector[C, EndPointsNR(3)]) → pic3B21NR
  65. Translate(pic2small, Vector[B, EndPointsNR(2)]) → pic2B12NR
  66. Translate(pic2small, Vector[B, EndPointsNR(5)]) → pic2B31NR
  67. Translate(pic1small, Vector[A, EndPointsNR(4)]) → pic1B22NR
  68. Translate(pic1small, Vector[A, EndPointsNR(6)]) → pic1B32NR
  69. Polygon({D, D + (2, 0), D + (2, 2), D + (0, 2)}) → q1
  70. Translate(q1, (2, 0)) → q2
  71. Translate(q1, (4, 0)) → q3
  72. Translate(pic1, Vector[CP11, D]) → pic1T1
  73. Translate(pic1, Vector[CP11, Vertex[q2, 1]]) → pic1T2
  74. Translate(pic1, Vector[CP11, Vertex[q3, 1]]) → pic1T3
  75. Translate(pic2, Vector[CP21, D]) → pic2T1
  76. Translate(pic2, Vector[CP21, Vertex[q2, 1]]) → pic2T2
  77. Translate(pic2, Vector[CP21, Vertex[q3, 1]]) → pic2T3
  78. Translate(pic3, Vector[CP31, Vertex[q3, 1]]) → pic3T3
  79. Translate(pic3, Vector[CP31, Vertex[q2, 1]]) → pic3T2
  80. Translate(pic3, Vector[CP31, D]) → pic3T1
  81. If(repYESNO, g(anim), anim - floor(anim)) → time
  82. Translate(pic1, Vector[CP11, PAnim1]) → pic1'
  83. Translate(pic2, Vector[CP21, PAnim2]) → pic2'
  84. Translate(pic3, Vector[CP31, PAnim3]) → pic3'
  85. If(repYESNO, 1 / 2, 1) → speed
  86. Translate(Element[{pic1small, pic2small, pic3small}, orderAnim(1)], Vector[Element[{A, B, C}, orderAnim(1)], E]) → pic4
  87. Translate(Element[{pic1small, pic2small, pic3small}, orderAnim(2)], Vector[Element[{A, B, C}, orderAnim(2)], F]) → pic5
  88. Translate(Element[{pic1small, pic2small, pic3small}, orderAnim(3)], Vector[Element[{A, B, C}, orderAnim(3)], G]) → pic6
  89. If(repYESNO, index3R, index3NR) → index3
  90. If(repYESNO, index2R, index2NR) → index2
  91. If(repYESNO, segsAbove(index2), segsAboveNR(index2)) → f
  92. If(repYESNO, segsBelow(index3), segsBelowNR(index3)) → h
  93. If(repYESNO, 328, 301) → onboardingX_{1}
  94. onboardingTextOffset(Corner[onboardingText_{1}, 1], Corner[onboardingText_{1}, 3], onboardingCase_{1}, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset_{1}
  95. If(repYESNO, EndPoints(12), EndPointsNR(3)) → InputPoint
  96. circlePixels(InputPoint, 12 + (7 * pulsing), Cor1, Cor3, (800, 500)) → pulsingObject
  97. Circle(Center1, 0.75) → CircleWhite1
  98. Circle(Center2, 0.75) → CircleWhite2
  99. Circle(Center3, 0.75) → CircleWhite3

AI Drawing Prompt Reference

Draw a probability tree diagram comparing outcomes with and without replacement. The diagram should include multiple nodes and connected lines, with nodes arranged from top to bottom. Lines represent the sequence of events. Construct by first creating the root node, then adding child nodes, and finally connecting the lines to clearly show different probability paths.
The prompt above was compiled from the original drawing commands and is for reference only.