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QUESTION 3 [3] (Parts (a) and (b) are separate). (a) Consider two events A and B. It is known that: . P[A] = 0.4 . P[BA '] = 0.3 . P[ABC] = 0.2 i. [6 pts] Are A and B independent? (Show your work clearly) ii. [6 pts] Are A and B collectively exhaustive? (Show your work clearly) (b) [13 pts] Consider three events X, Y and Z. It is known that (i) X and Y are independent, (ii) X and Z are mutually exclusive, (iii) P[X]=P[Y]=0.4, P[Z]=0.4 and P[Z|Y]=0.5 . Find the probability P[X+Y+Z]. Attach File Browse Local Files Browse Content Collection