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"si A et B sont deux évènements indépendants, alors Abarre et B sont aussi indépendantes"(A union B) U (Abarre union =B=> P(B) = P(A union B)+ P(Abarre union B)=> P(Abarre union B)= P(B) -P(A union B)Or, A et B sont indépendants. D'où P(A union B) =P(A) *P(B)Donc P(Abarre union B)=P(B)-P(A)P(B)=P(B)[1-P(A)] =P(B)P(Abarre) =P(Abarre)*P(B)=> A barre et B sont indépendants
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