(a) Consider two events A and B It is known that p A 0 4 P BA c 0 3 p AB C 0 2 6 pts Are A and B independent (Show your work clearly) 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

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Question: (a) Consider two events A and B. It is known that: p[A]=0.4 P[BA^c]=0.3 p[AB^C]=0.2 [6 pts] Are A and B independent? (Show your work clearly)

(a) Consider two events A and B. It is known that:

p[A]=0.4
P[BA^c]=0.3
p[AB^C]=0.2

[6 pts] Are A and B independent? (Show your work clearly)
[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].

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