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. Let pX denote the success probability for X. Find pX.
b. Let pY denote the success probability for Y. Find pY.
c. Let pZ denote the success probability for Z. Find pZ.
d. Is it possible for both X and Y to equal 1?
e. Does pZ = pX + py?
f. Does Z = X + Y? Explain.
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