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Prove
1.P[A|B]=(P[A∩B])/(P[B]) P[A│B]∙P[B]=P[A∩B] 2.P[B|A]=(P[B∩A])/(P[A]) P[B│A]∙P[A]=P[B∩A]
3.P[B│A]∙P[A]=P[B∩A]=P[A∩B]=P[A|B]∙P[B]
4.P[B|A]=(P[A|B]∙P[B])/(P[A])
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Prove
1.P[A|B]=(P[A∩B])/(P[B]) P[A│B]∙P[B]=P[A∩B] 2.P[B|A]=(P[B∩A])/(P[A]) P[B│A]∙P[A]=P[B∩A]
3.P[B│A]∙P[A]=P[B∩A]=P[A∩B]=P[A|B]∙P[B]
4.P[B|A]=(P[A|B]∙P[B])/(P[A])