Prove that
(i) `P(A)=P(AcapB)+P(AcapbarB)`
(ii) `P(AcupB)=P(AcapB)+P(AcapbarB)+P(barAcapB)`

Given that P(A)=.43,P(B)=.34 P(AcapB)=.15. Find(i) P(AcapbarB) (ii) P(AcupB) (iii) P(barAcapbarB) (iv) P(barAcupbarB)

If A and B are mutually exclusive events, P(A)=0.35 amd P(B)=0.45, then find (i) P(A') (ii) P(B') (iii) P(AcupB) (iv) P(AcapB) (v) P(AcapB') (vi) P(A'cupB')

If A and B are mutually exclusive events, P(A)=0.35 amd P(B)=0.45, then find (i) P(A') (ii) P(B') (iii) P(AcupB) (iv) P(AcapB) (v) P(AcapB') (vi) P(A'cupB')

If A and B are mutually exclusive events, P(A) = 0.35 and P(B)= 0.45 , find (i) P(A') (ii) P(B') (iii) P(AcupB) (iv) P(AcapB) (v) P(AcapB') (vi) P(A'capB')

If P(A)=0.5, P(B)=0.3, P(AcapB) =0.25. Find P(AcupB)

If A, B C are three events associated with a random experiment, prove that P(AcupBcupC)=P(A)+P(B)+P(C)-P(AcapB)-P(AcapC)- P(BcapC)+ P(AcapBcapC) .

P(A)=0.35,P(B)=0.73,P(AcapB)=0.14 ,find P(barAcapB),P(AcupB),P(barAcupbarB) .

The accompanying Venn diagram shows three events, A,B, and C, also the probabilities of the various intersections (for instance, P(AcapB)=.07 ). Determine (i) P(A) (ii) P(BcapC') (iii) P(AcupB) (iv) P(AcapB') (v) P(BcapC) (vi) Probability of exactly one of the three occurs.

A and B are two events such that P(A)=0.54, P(B)=0.69 and P(A,C, B) =0.35. Find (i) P(AcupB) (ii) P(A'capB') (iii) P(AcapB') (iv) P(BcapA')

If 4P(A) = 6P(B) = 10P(AcapB)=1 , then P(B/A)