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Probability Venn Diagram: Rectangle

Probability Venn Diagram: Rectangle
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2012-01-29 19:58
Probability & StatisticsGeometric ConstructionGraphing
In collections Probability Venn Diagrams
This example demonstrates how to represent a probability Venn diagram using a rectangle with proportionally-sized regions. Key math concepts include probability theory, set theory, and area calculations of geometric figures. GeoGebra commands and objects used in construction are Line, Circle, Segment, If, Midpoint, Polygon. Suitable for high school and above students learning about set relationships and area representation in probability 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