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Explore Conditional Probability

Explore Conditional Probability
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2013-12-30 05:45
CalculusProbability & StatisticsGeometric Construction
In collections statistics
This example uses GeoGebra to demonstrate the concept of conditional probability. By adjusting parameters, observe how the probability of event A changes given that event B has occurred. Key mathematical concepts include the definition and calculation of conditional probability. The construction uses commands such as Circle, Polygon, If, Segment, Intersect, and Point. Suitable for high school probability and statistics courses.

GeoGebra Commands & Parameters

  1. Circle((-2, 0), 3) → c
  2. Circle((2, 0), 3) → d
  3. Polygon((-6, 4), (-6, -4), (6, -4), (6, 4)) → r, a, b, e, f
  4. If(n ≟ 1, c, d) → set1
  5. If(n ≟ 1, d, c) → set2
  6. Segment(A_1, C) → seg2
  7. Segment(A_1, B_1) → seg1
  8. Segment(D, E) → seg3
  9. Segment(D, F) → seg4
  10. Segment(G, H) → seg5
  11. Segment(G, I) → seg6
  12. Intersect(c, d) → M, N, ,
  13. Segment(M, N) → line
  14. Point(d) → O
  15. Point(c) → P
  16. CircumcircleArc(M, P, N) → p
  17. CircumcircleArc(M, O, N) → q
  18. Polygon((-6, 4), (-6, -4), (6, -4), (6, 4)) → rect, m_1, s, t, a_1
  19. Text(If[n ≟ 1, "A", "B"]) → text1
  20. Text(If[n ≟ 1, "A'", "B'"]) → text2
  21. Text(If[n ≟ 1, "B", "A"]) → text3
  22. Text(If[n ≟ 1, "B", "A"]) → text5
  23. Text(If[n ≟ 1, "B'", "A'"]) → text4
  24. Text(If[n ≟ 1, "B'", "A'"]) → text6
  25. Text(If[n ≟ 1, "P(A and B')", "P(B and A')"]) → text8
  26. Text(If[n ≟ 1, "P(A' and B)", "P(B' and A)"]) → text9
  27. Text(If[n ≟ 1, "P(A and B)", "P(B and A)"]) → text7
  28. Text(If[n ≟ 1, "P(A' and B')", "P(B' and A')"]) → text10
  29. If(n ≟ 1, FractionText[A / total], FractionText[B / total]) → prob1
  30. If(n ≟ 1, FractionText[notA / total], FractionText[notB / total]) → prob1'
  31. If(n ≟ 1, FractionText[AandB / A], FractionText[AandB / B]) → prob2g1
  32. If(n ≟ 1, FractionText[AnotB / A], FractionText[BnotA / B]) → prob2'g1
  33. If(n ≟ 1, FractionText[BnotA / notA], FractionText[AnotB / notB]) → prob2g1'
  34. If(n ≟ 1, FractionText[notAnotB / notA], FractionText[notAnotB / notB]) → prob2'g1'
  35. FractionText(AandB / total) → prob1and2
  36. If(n ≟ 1, FractionText[AnotB / total], FractionText[BnotA / total]) → prob1and2'
  37. If(n ≟ 1, FractionText[BnotA / total], FractionText[AnotB / total]) → prob1'and2
  38. FractionText(notAnotB / total) → prob1'and2'
  39. If(n ≟ 1, "P(A)", "P(B)") → notation1
  40. If(n ≟ 1, "P(A')", "P(B')") → notation2
  41. If(n ≟ 1, "P(B|A)", "P(A|B)") → notation3
  42. If(n ≟ 1, "P(B'|A)", "P(A'|B)") → notation4
  43. If(n ≟ 1, "P(B|A')", "P(A|B')") → notation5
  44. If(n ≟ 1, "P(B'|A')", "P(A'|B')") → notation6