Question

Uzasadnij, że jeśli P(C)>0, to P[(AuB)|C]=P(A|C)+P(B|C)-P[(A iloczyn B)|C)

Answer 1

P[(AuB)nC]/P(C) = P(AnC)/P(C)+P(BnC)/P(C)-P(AnBnC)/P(C)   /*P(C)
L=P(AuB)+P(C)-P(AuBuC)=P(A)+P(B)-P(AnB)+P(C)-P(AuBuC)
L=P(A)+P(B)-P(AnB)+P(C)-P(AuBuC)=P(A)+P(B)+P(C)-P(AnB)-P(AuBuC)
P=P(A)+P(B)+P(C)-P(AnB)-P(AuBuC)
L=P