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Conditional Probability & Hypergeometric Distribution Demo

Conditional Probability & Hypergeometric Distribution Demo
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2018-07-04 15:47
Probability & StatisticsMatrixGeometric Construction
In collections Pearson Maths A level Statistics and Mechanics 2 Pearson Maths A level Statistics and Mechanics 2 Pearson Maths A level Statistics and Mechanics 2
This example dynamically demonstrates the calculation of conditional probability and the application of the hypergeometric distribution using GeoGebra. It involves core math concepts like conditional probability, hypergeometric distribution, matrix operations, and integral calculations. The construction utilizes commands/objects such as Point, Circle, Intersect, Integral, IntegralBetween, Polygon, PolyLine, LaTeX, IndexOf, Defined for interactive graphics and formula display. Suitable for high school and above learners to understand the application of probability statistics combined with geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(A, 2) → c
  3. Intersect(c, xAxis, 2) → B
  4. Circle(B, 2) → d
  5. Intersect(c, d, 2) → C
  6. Circle(C, 2) → e
  7. Intersect(c, d, 1) → D
  8. Intersect(d, e, 1) → E
  9. Intersect(c, e, 2) → F
  10. Intersect(c, xAxis, 1) → G
  11. Intersect(d, xAxis, 2) → H
  12. Integral(h, -3, -1) → a
  13. IntegralBetween(h, g, -1, 0) → b
  14. Integral(hh, -3, -2) → i
  15. Integral(p, -2, -1) → j
  16. IntegralBetween(g, p, -1, 0) → k
  17. IntegralBetween(h, p, 0, 1) → l
  18. IntegralBetween(g, h, 0, 1) → m
  19. Integral(g, 1, 3) → n
  20. Integral(gg, 2, 3) → o
  21. Integral(p, 1, 2) → q
  22. IntegralBetween(hh, pp, -2, 0) → r
  23. IntegralBetween(gg, pp, 0, 2) → s
  24. IntegralBetween(p, hh, -2, -1) → t
  25. IntegralBetween(gg, hh, -1, 0) → u
  26. IntegralBetween(hh, gg, 0, 1) → v
  27. IntegralBetween(p, gg, 1, 2) → w
  28. Integral(p, -1, 1) → a_1
  29. Integral(gg, -1, 0) → b_1
  30. Polygon((-4.5, 2.5), (4.5, 2.5), (4.5, -5), (-4.5, -5)) → poly1, f_1, g_1, h_1, i_1
  31. PolyLine((-4.5, 2.5), (4.5, 2.5), (4.5, -5), (-4.5, -5), (-4.5, 2.5)) → j_1
  32. Integral(hh, 0, 1) → ccc
  33. LaTeX("A \cap \left( B \cup C \right)' ") → C1
  34. LaTeX("B\cap \left( A \cup C \right)' ") → C2
  35. LaTeX("C \cap \left( A \cup B \right)' ") → C3
  36. LaTeX("A \cap B") → C4
  37. LaTeX("B \cap C") → C5
  38. LaTeX("A \cap C") → C6
  39. LaTeX("A \cap B \cap C") → C7
  40. LaTeX("\left(A \cup B \cup C\right)' ") → C8
  41. LaTeX("A") → C9
  42. LaTeX("B") → C10
  43. LaTeX("C") → C11
  44. LaTeX("C' ") → C13
  45. LaTeX("\left( B \cup C \right)' ") → C15
  46. LaTeX("\left( A \cup C \right)' ") → C16
  47. LaTeX("\left( A \cup B \right)' ") → C17
  48. LaTeX("A \cap C' ") → C19
  49. LaTeX("B \cap C' ") → C20
  50. LaTeX("B\cap A' ") → C21
  51. LaTeX("C \cap A' ") → C22
  52. LaTeX("C \cap B' ") → C23
  53. LaTeX("A \cap B' ") → C24
  54. LaTeX("\left(A\cup B\right) \cap C' ") → C25
  55. LaTeX("\left(B\cup C\right) \cap A' ") → C26
  56. LaTeX("\left(A\cup C\right) \cap B' ") → C27
  57. LaTeX("A' ") → C12
  58. LaTeX("B' ") → C14
  59. LaTeX("\left(A \cap B \right) \cup \left(A \cap C \right) \cup \left(B \cap C \right)") → C28
  60. LaTeX("\text{Try buttons 1 and 2}") → C18
  61. IndexOf(true, L_1) → d_1
  62. Defined(d_1) → e_1

AI Drawing Prompt Reference

Draw a dynamic illustration showing conditional probability and hypergeometric distribution, featuring two concentric circles and their intersection points, multiple integral regions highlighted differently, and display related probability formulas and set operation symbols to demonstrate the application of conditional probability and hypergeometric distribution.
The prompt above was compiled from the original drawing commands and is for reference only.