📊 Visual Bounds
🔗 Intersection P(A∩B)
max(0, P(A)+P(B)−1) ≤ P(A∩B) ≤ min(P(A), P(B))
Lower: 0.00
Upper: 0.40
🔗 Union P(A∪B)
max(P(A), P(B)) ≤ P(A∪B) ≤ min(1, P(A)+P(B))
Lower: 0.50
Upper: 0.90
💡 Why These Bounds?
Upper bound for intersection: A∩B ⊆ A and A∩B ⊆ B
→ P(A∩B) ≤ min(P(A), P(B))
Lower bound for intersection: From inclusion-exclusion
P(A∪B) = P(A) + P(B) − P(A∩B) ≤ 1
→ P(A∩B) ≥ P(A) + P(B) − 1