When a certain glaze is applied to a ceramic surface, the probability is 5% that there will be discoloration, 20% that there will be a crack, and 23% that there will be either discoloration or a crack, or both. Let X = 1 if there is discoloration, and let X = 0 otherwise. Let Y = 1 if there is a crack, and let Y = 0 otherwise. Let Z = 1 if there is either discoloration or a crack, or both, and let Z = 0 otherwise.

a. Let denote the success probability for X. Find .

b. Let denote the success probability for Y. Find .

c. Let denote the success probability for Z. Find .

d. Are X and Y independent?

e. Does

f. Does Z = XY? Explain.




a) = 0.05

(b) = 0.20

(c) = 0.23

(d) Yes, it is possible for there to be both discoloration and a crack.

(e) No.

(f)No. If the surface has both discoloration and a crack, then ????= 1, ????= 1, and ????= 1, but ????+ ????= 2.

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