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Probability and Tree Diagram Demo

Probability and Tree Diagram Demo
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2019-08-06 04:36
Probability & StatisticsGeometric ConstructionGraphing
This example demonstrates probability tree diagrams interactively, visually showing how probabilities combine through event occurrences; core math concepts include probability calculation, independence of events, and tree diagram construction; GeoGebra commands used are Sequence, Center, If, Point, and Segment for creating sequences, centering, conditional logic, point placement, and line segment drawing; suitable for high school mathematics teaching, particularly introductory probability & statistics and complex event analysis.

GeoGebra Commands & Parameters

  1. Sequence(Circle[Element[Centre01, i], BallRadius], i, 2, NoB + 1) → BallBlueList01
  2. Center(Element[BallBlueList01, 1]) → AA
  3. Sequence(Circle[Element[Centre11, i], BallRadius], i, 2, NoB) → BallBlueList11
  4. Sequence(Circle[Element[Centre12, i], BallRadius], i, 2, NoB + 1) → BallBlueList12
  5. Sequence(Circle[Element[Centre21, i], BallRadius], i, 2, NoB - 1) → BallBlueList21
  6. Sequence(Circle[Element[Centre22, i], BallRadius], i, 2, NoB) → BallBlueList22
  7. Sequence(Circle[Element[Centre24, i], BallRadius], i, 2, NoB + 1) → BallBlueList24
  8. Sequence(Circle[Element[Centre23, i], BallRadius], i, 2, NoB) → BallBlueList23
  9. Sequence(If[step ≤ 10, (FindCor(step, 0, 10, x(Element[Tree01Point, i]), x(Element[Tree02Point, i])), FindCor(step, 0, 10, y(Element[Tree01Point, i]), y(Element[Tree02Point, i]))), Element[Tree02Point, i]], i, 1, 2) → Tree02MovingPoint
  10. Sequence(Segment[Element[Tree01Point, i], Element[Tree02MovingPoint, i]], i, 1, 2) → TreeLine01
  11. Sequence(If[step < 35, Element[Tree03Point, i], If[step > 45, Element[Tree04Point, i], (FindCor(step, 35, 45, x(Element[Tree03Point, i]), x(Element[Tree04Point, i])), FindCor(step, 35, 45, y(Element[Tree03Point, i]), y(Element[Tree04Point, i])))]], i, 1, 4) → Tree04MovingPoint
  12. Sequence(Segment[Element[Tree03Point, i], Element[Tree04MovingPoint, i]], i, 1, 4) → TreeLine02
  13. If(step < 20, Element[Centre11, NoB + 1], If[step > 30, C11a, (FindCor(step, 20, 30, x(Element[Centre11, NoB + 1]), x(C11a)), FindCor(step, 20, 30, y(Element[Centre11, NoB + 1]), y(C11a)))]) → C11aMove
  14. If(step < 20, Element[Centre12, NoB + 2], If[step > 30, C12a, (FindCor(step, 20, 30, x(Element[Centre12, NoB + 2]), x(C11a)), FindCor(step, 20, 30, y(Element[Centre12, NoB + 2]), y(C12a)))]) → C12aMove
  15. If(step < 50, Element[Centre21, NoB], If[step > 60, C21b, (FindCor(step, 50, 60, x(Element[Centre21, NoB]), x(C21b)), FindCor(step, 50, 60, y(Element[Centre21, NoB]), y(C21b)))]) → C21bMove
  16. If(step < 50, Element[Centre23, NoB + 1], If[step > 60, C23b, (FindCor(step, 50, 60, x(Element[Centre23, NoB + 1]), x(C23b)), FindCor(step, 50, 60, y(Element[Centre23, NoB + 1]), y(C23b)))]) → C23bMove
  17. If(step < 50, Element[Centre24, NoB + 3], If[step > 60, C24b, (FindCor(step, 50, 60, x(Element[Centre24, NoB + 3]), x(C24b)), FindCor(step, 50, 60, y(Element[Centre24, NoB + 3]), y(C24b)))]) → C24bMove
  18. If(step < 50, Element[Centre22, nb + 1], If[step > 60, C22b, (FindCor(step, 50, 60, x(Element[Centre22, nb + 1]), x(C22b)), FindCor(step, 50, 60, y(Element[Centre22, nb + 1]), y(C22b)))]) → C22bMove
  19. Sequence(Circle[Element[BlueSelectedMovingCentreList, i], BallRadius], i, 1, 1) → BallBlueSelectedList01
  20. Sequence(Circle[Element[RedSelectedMovingCentreList, i], BallRadius], i, 2, 5) → BallRedSelectedList02
  21. Sequence(Circle[Element[RedSelectedMovingCentreList, i], BallRadius], i, 1, 1) → BallRedSelectedList01
  22. Sequence(Circle[Element[BlueSelectedMovingCentreList, i], BallRadius], i, 2, 5) → BallBlueSelectedList02
  23. Sequence(Circle[Element[Centre01, i], BallRadius], i, NoB + 2, nb + 1) → BallRedList01
  24. Sequence(Circle[Element[Centre11, i], BallRadius], i, NoB + 2, nb + 1) → BallRedList11
  25. Sequence(Circle[Element[Centre12, i], BallRadius], i, NoB + 3, nb + 1) → BallRedList12
  26. Sequence(Circle[Element[Centre22, i], BallRadius], i, NoB + 2, nb) → BallRedList22
  27. Sequence(Circle[Element[Centre23, i], BallRadius], i, NoB + 3, nb + 1) → BallRedList23
  28. Sequence(Circle[Element[Centre24, i], BallRadius], i, NoB + 4, nb + 1) → BallRedList24
  29. Sequence(Circle[Element[Centre21, i], BallRadius], i, NoB + 2, nb + 1) → BallRedList21
  30. Point(tempL11) → Z17
  31. Segment(Z17, Z08) → i

AI Drawing Prompt Reference

Draw a probability tree diagram with two initial events, each with two possible outcomes. Event A has blue and red outcomes, and event B has two possible outcomes under each result of A. Use segments to connect each event's outcomes, forming a tree structure. Place circles at each outcome point to represent the probability of the event occurring. As the step changes, the outcome points will move, demonstrating how probabilities combine through event occurrences.
The prompt above was compiled from the original drawing commands and is for reference only.