{"id":"probability","domain":"probability-statistics","type":"Concept","title":"Probability","slug":"probability","url":"/mathematics/probability-statistics/probability/","summary":"Mathematical framework for chance and uncertainty. Formalised by Kolmogorov's axioms (1933). Origins in Pascal-Fermat correspondence (1654).","formal_definition":"Kolmogorov axioms: P(A)≥0; P(S)=1; P(A∪B)=P(A)+P(B) for mutually exclusive A,B.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Kolmogorov, A.N. (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer."},{"tier":1,"citation":"Feller, W. (1968). An Introduction to Probability Theory and Its Applications. Vol. 1, 3rd ed. Wiley."},{"tier":2,"citation":"Hacking, I. (2006). The Emergence of Probability. 2nd ed. Cambridge University Press."},{"tier":3,"citation":"Devlin, K. (2008). The Unfinished Game. Basic Books."}],"relationships":[{"type":"historical_origin","target":null,"label":"Pascal-Fermat correspondence 1654"},{"type":"related_to","target":"fermats-last-theorem","label":"Fermat's Last Theorem — same Fermat"},{"type":"formalised_via","target":"integral","label":"Integral — measure theory"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.5"}