udowadnianie wzoru andrzej: Udowodnij wzor P(A u B u C)= P(A)+P(B)+P(C)−P(AnC)−P(BnC)−P(AnB)+P(AnBnC)

Mila: A∪B∪C=A∪(B∪C) P(A∪(B∪C))=P(A)+P(B∪C)−P(A∩(B∪C))= =P(A)+P(B)+P(C)−P(B∩C)−P((A∩B) ∪(A∩C))= =P(A)+P(B)+P(C)−P(B∩C)−[P(A∩B)+P(A∩C)−P(A∩B∩A∩C)]= =P(A)+P(B)+P(C)−P(B∩C)−P(A∩B)−P(A∩C)+P(A∩B∩C)