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Interactive 3D/Probability Space
Probabilities
P(A)0.50
P(B)0.40
P(A∩B)0.20
Capped at min(P(A), P(B)) = 0.40
Derived Values
P(A)0.500
P(B)0.400
P(A∩B)0.200
P(A∪B)0.700
P(A|B)0.500
P(B|A)0.400
Quick Presets
Key Formulas
P(A∪B) = P(A) + P(B) − P(A∩B)
P(A|B) = P(A∩B) / P(B)
Independent if P(A∩B) = P(A)·P(B)

Probability Space - Interactive Visualization

Probability theory begins with a sample space Ω and events (subsets). The Venn diagram of A and B makes intersection, union, and conditional probability concrete. Adjusting P(A), P(B), and P(A∩B) shows all derived probabilities live: P(A∪B) = P(A)+P(B)-P(A∩B), and P(A|B) = P(A∩B)/P(B). When P(A∩B) = P(A)·P(B), events are independent.

  • Drag P(A), P(B), P(A∩B) to see all derived probabilities update
  • See P(A∪B), P(A|B), P(B|A) computed instantly from Venn diagram
  • Detect independence when P(A∩B) ≈ P(A)·P(B)
  • Understand complementary events and exhaustive partitions
  • Foundation for naive Bayes, Bayesian networks, and probabilistic models

Part of the EngineersOfAI Interactive 3D - free interactive visualizations covering every major concept in machine learning and AI engineering. Hover any element for a plain-English explanation. No code required.