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If A, B, C are three events associated with a random experiment prove that `P(AuuBuuC)=P(A)+P(B)+P(C)-P(AnnC)-P(BnnC)+P(AnnBnnC)`

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We know that
P(A∪B)=P(A)+P(B)−P(A∩B)
Let us take B∪C to be another event R
∴P(A∪B∪C)=P(A∪R)
=P(A)+P(R)−P(A∩R)
=P(A)+P(B∪C)−P(A∩(B∪C))
=P(A)+P(B)+P(C)−P(B∩C)−[P(A∩B)+P(A∩C)−P(A∩B∩C)] =P(A)+P(B)+P(C)−P(B∩C)−P(A∩B)−P(A∩C)+P(A∩B∩C)
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If A;B and C are three events associated with a random experiments then P(A uu B uu C)=P(A)+P(B)+P(C)-P(A nn B)-P(B nn C)-P(C nn A

If A and B are two events associated with a random experiment; then P(A uu B)=P(A)+P(B)-P(A nn B)

If A and B are independent events associated with a random experiment; then P(AnB)=P(A)P(B)

If A and B are two events associated with a random experiment; then P((bar(A))/(B))=1-P((A)/(B))

If A and B are two events associated with a random experiment such that P(A uu B)=0.8,P(A nn B)=0.3 and P(A)=0 ,find P(B)

If A and B are two events associated with a random experiment such that P(A)=0.3,P(B)=0.4 and P(A uu B)=0. find P(A nn B)

For any three events A,B and C, prove that,P(A uu B uu C)=P(A)+P(B)+P(C)-P(A nn B)-P(B nn C)-P(C nn A)+P(A nn B nn C)

Let P(E) denote the probability of occurrence of event E. If A and B are two events associated with an experiment such that |[P(A)-1,P(B),-P(A nn B)],[P(B),-P(A nn B),P(A)-1],[-P(A nn B),P(A)-1,P(B)]|=0 then (A) P(A uu B)=1 (B) P(A/B)=(P(A)+P(B)-1)/(P(B)) (C) if A sub B then P(B)=P(A uu B) (D) if A sub B then P(A)=1

If A and B are two events associated with a random experiment such that P(A)=0.5,P(B)=0.3 and P(A nn B)=0.2, find P(A uu B)

Let P(E) denote the probability of occurrence of event E. If A and B are two events associated with an experiment such that, |[P(A)-1,P(B),-P(A nn B)],[P(B),-P(A nn B),P(A)-1],[-P(A nn B),P(A)-1,P(B)]|=0 ,then (A) P(A uu B)=1 (B) P(A/B)=(P(A)+P(B)-1)/(P(B))

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