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Conditional Probability and 'AND'/'OR' Events

Conditional Probability and 'AND'/'OR' Events
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2015-11-03 21:49
FunctionCoordinate GeometryProbability & Statistics
This example demonstrates conditional probability and 'AND'/'OR' events using a Venn diagram. It covers key concepts such as probability and fractions. The construction uses GeoGebra commands like Line, Circle, Segment, If, Midpoint, Polygon. Suitable for high school and above students learning probability and statistics.

GeoGebra Commands & Parameters

  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