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条件概率与“与”、“或”事件的概率

条件概率与“与”、“或”事件的概率
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2015-11-03 21:49
函数解析几何概率统计
该范例通过维恩图演示条件概率和“与”、“或”事件的概率。它涉及概率、分数等核心数学概念。使用了Line, Circle, Segment, If, Midpoint, Polygon等GeoGebra命令进行构造。适合高中及以上学生学习概率统计。

GeoGebra 命令及参数

  1. Line(A, B) → c
  2. Circle(C, r1) → g
  3. Circle(D, r2) → e
  4. Segment(C, D) → dist
  5. If(x(D) - x(C) ≤ r1 - r2, Min[a, b], (r1^(2) * θ) + (r2^(2) * α) - (h * ((r1^(2) - h^(2))^(0.5) + (r2^(2) - h^(2))^(0.5)))) → intersection1
  6. If(x(D) - x(C) ≤ r2 - r1, Min[a, b], (r1^(2) * θ) + (r2^(2) * α) - (h * ((r1^(2) - h^(2))^(0.5) + (r2^(2) - h^(2))^(0.5)))) → intersection2
  7. If(r2 + r1 < x(D) - x(C), 0, If[r2 ≥ r1, intersection2, intersection1]) → IntersectArea
  8. Midpoint(C, D) → E
  9. Polygon((x(E) - φ^(0.5) / 2, y(E) - 1 / ((2 * φ^(0.5)))), (x(E) - φ^(0.5) / 2, y(E) + 1 / ((2 * φ^(0.5)))), (x(E) + φ^(0.5) / 2, y(E) + 1 / ((2 * φ^(0.5)))), (x(E) + φ^(0.5) / 2, y(E) - 1 / ((2 * φ^(0.5))))) → poly1, f, i, j, k
  10. Circle(D, r2) → p
  11. Polygon(F, G, H, I) → poly2, f_1, g_1, h_1, i_1
  12. If(logooff < 4.5, 0, (2 * (logooff - 4.5))) → logooffopa
  13. Circle(C_1, r1_1) → g_2
  14. Circle(D_1, r2_1) → e_1
  15. Segment(C_1, D_1) → dist_1
  16. If(x(D_1) - x(C_1) ≤ r1_1 - r2_1, Min[a, b], (r1_1^(2) * θ_1) + (r2_1^(2) * α_1) - (h_2 * ((r1_1^(2) - h_2^(2))^(0.5) + (r2_1^(2) - h_2^(2))^(0.5)))) → intersection1_1
  17. If(x(D_1) - x(C_1) ≤ r2_1 - r1_1, Min[a, b], (r1_1^(2) * θ_1) + (r2_1^(2) * α_1) - (h_2 * ((r1_1^(2) - h_2^(2))^(0.5) + (r2_1^(2) - h_2^(2))^(0.5)))) → intersection2_1
  18. If(r2_1 + r1_1 < x(D_1) - x(C_1), 0, If[r2_1 ≥ r1_1, intersection2_1, intersection1_1]) → IntersectArea_1
  19. Midpoint(C_1, D_1) → E_1
  20. Circle(D_1, r2_1) → p_1