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Probability and conditional information

Probability and conditional information · Diagrams

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Complement, disjointness and conditional reference sets

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Source proof sketches: E lies in sample space S, with its complement the rest; disjoint A and B have no common outcomes; for conditional probability given B, the entire B region is the reference set and its overlap with A is favourable. Blue marks the intersection and orange marks the rest of B. Areas are schematic, not numerical probabilities. The union double-counting overlap uses the preceding intersection construction.
Source proof sketches: E lies in sample space S, with its complement the rest; disjoint A and B have no common outcomes; for conditional probability given B, the entire B region is the reference set and its overlap with A is favourable. Blue marks the intersection and orange marks the rest of B. Areas are schematic, not numerical probabilities. The union double-counting overlap uses the preceding intersection construction.
Source proof sketches: E lies in sample space S, with its complement the rest; disjoint A and B have no common outcomes; for conditional probability given B, the entire B region is the reference set and its overlap with A is favourable. Blue marks the intersection and orange marks the rest of B. Areas are schematic, not numerical probabilities. The union double-counting overlap uses the preceding intersection construction.
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