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 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.