# Probability Axiom

Thesynonymprobabilitystatistics(mathematicalterm)generallyreferstotheaxiomofprobability.

## Briefintroduction

Thisaxiomcanalsobeexpressedinreverse:"Theeventwiththehighestprobabilityinarandomsamplingisthemostlikelytooccur.)event".

"Onerandomsampling"isatermusedinstatistics.Itallowsyoutorandomlytakeoutoneofmanyobjectswithoutsubjectiveprejudice(insomecases,abatchofsamplingisunifiedasoneExperiment)asasampleforresearch.Thesamplinghereisonlyperformedonce,anditisnotallowedtobedissatisfiedthefirsttime,andthenmakeanothersample.

Theword"mostlikelytoappear"hasasimplemeaning,andithasatasteof"practice".

Theword"probability"hasanabstractmeaningandatasteof"rationality".

## Researchhistory

ProbabilityAxioms(ProbabilityAxioms),becauseitsinventorisAndreiKolmogorov,alsoknownasKolmogorovLoveAxiom.WhentheprobabilityP(E)ofaneventEisdefinedinthe"universe"(universe)orthesamplespaceOmegaofallpossiblebasicevents,theprobabilityPmustsatisfythefollowingKolmogorovaxiom.Itcanalsobesaidthatprobabilitycanbeinterpretedasameasuredefinedonthesigmaalgebra($\sigma-Algebra\right)ofasubsetofthesamplespace.Thosesubsetsareevents,sothatthemeasureofallsetsis1.Thispropertyisimportantbecauseitbringsupthenaturalconceptofconditionalprobability.Foreachnon-zeroprobabilityA,anotherprobabilitycanbedefinedinspace:P\left(B\vertA\right)=\left\{P\left(B\capA\right)\overP\left(A\right)\right\}Thisisusuallyreadas"givenSettheprobabilityofBwhenA".IftheconditionalprobabilityofBisthesameastheprobabilityofBwhenAisgiven,thenAandBaresaidtobeindependent.Whenthesamplespaceisfiniteorcountableinfinite,theprobabilityfunctioncanalsodefineitsvalueintermsofbasicevents\\left\{e_1\\right\},\\left\{e_2\\right\},...,here\Omega=\\left\{e_1,e_2,...\\right\}.$