A certain brand of dinnerware set comes in three colors: red, white, and blue. Twenty percent of customers order the red set, 45% order the white, and 35% order the blue. Let X = 1 if a randomly chosen order is for a red set, let X = 0 otherwise; let Y = 1 if the order is for a white set, let Y = 0 otherwise; let Z = 1 if it is for either a red or white set, and let Z = 0 otherwise.
(a) 
= 0.2
b) 
= 0.45
(c) 
(d) No. If the order is for a red set, it cannot also be for a white set.
(e) Yes. 
(f) Yes. If the set is red, then X = 1, Y = 0, and ???? = 1, so ???? = ???? + ???? . If the set is white, then ???? = 0, ???? = 1, and ???? = 1, so ???? = ???? + ???? . If the set is blue, then ???? = 0, ???? = 0, and ???? = 0, so ???? = ???? + ???? .
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