引用:
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作者polar168
∩交集
∪聯集
P(A ∪ B ∪ C)
=P(A ∪ B) + P(C) - P[(A ∪ B)∩ C]
=P(A)+P(B)-P(A ∩ B)+P(C)-P((A ∪ B)∩ C)
=P(A)+P(B)+P(C)-P(A ∩ B)-P((A ∩ C)∪(B ∩ C))
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P(A)+P(B)+P(C)-P(A ∩ B)-P((A ∩ C)∪(B ∩ C))
=P(A)+P(B)+P(C)-P(A ∩ B)-[P(A ∩ C)+P(B ∩ C)-P((B ∩ C)∩(A ∩ C))]
=P(A)+P(B)+P(C)-P(A ∩ B)-P(A ∩ C)-P(B ∩ C)+P((B ∩ C)∩(A ∩ C))
=P(A)+P(B)+P(C)-P(A ∩ B)-P(A ∩ C)-P(B ∩ C)+P(A ∩B ∩ C)