Formel von Bayes

P ( A | B ) = P ( A ) ⋅ P ( B | A ) P ( A ) ⋅ P ( B | A ) + P ( A ¯ ) ⋅ P ( B | A ¯ ) , MathType@MTEF@& 053;@& 053;@+= feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVu0Je9sqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabe qaamaaeaqbaaGcbaGaamiuamaabmaabaGaamyqamaaeeaabaGaamOq aaGaay5bSdaacaGLOaGaayzkaaGaeyypa0JaaeiiamaalaaabaGaam iuamaabmaabaGaamyqaaGaayjkaiaawMcaaiabgwSixlaadcfadaqa daqaaiaadkeadaabbaqaaiaadgeaaiaawEa7aaGaayjkaiaawMcaaa qaaiaadcfadaqadaqaaiaadgeaaiaawIcacaGLPaaacqGHflY1caWG qbWaaeWaaeaadaabcaqaaiaadkeaaiaawIa7aiaadgeaaiaawIcaca GLPaaacqGHRaWkcaWGqbWaaeWaaeaadaqdaaqaaiaadgeaaaaacaGL OaGaayzkaaGaeyyXICTaamiuamaabmaabaWaaqGaaeaacaWGcbaaca GLiWoadaqdaaqaaiaadgeaaaaacaGLOaGaayzkaaaaaiaabccacaqG GaGaaeiiaiaacYcaaaa@688C@ falls gilt: P ( A ) ≠ 0, P ( A ¯ ) ≠ 0, P ( B ) ≠ 0 MathType@MTEF@& 053;@& 053;@+= feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVu0Je9sqqrpepC 0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yq aqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabe qaamaaeaqbaaGcbaGaamiuamaabmaabaGaamyqaaGaayjkaiaawMca aiabgcMi5kaaicdacaGGSaGaaeiiaiaadcfadaqadaqaamaanaaaba GaamyqaaaaaiaawIcacaGLPaaacqGHGjsUcaaIWaGaaiilaiaabcca caWGqbWaaeWaaeaacaWGcbaacaGLOaGaayzkaaGaeyiyIK