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条件概率探索

条件概率探索
几何画板及绘图内容加载中，请稍等……
2013-12-30 05:45
微积分概率统计几何作图
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本范例通过几何画板演示条件概率的概念。通过调整参数，观察事件A在事件B发生条件下的概率变化。涉及的核心数学概念包括条件概率的定义及其计算方法。使用了Circle, Polygon, If, Segment, Intersect, Point等GeoGebra命令进行构造。适合高中数学概率统计课程使用。

GeoGebra 命令及参数

  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