A soft drink factory uses filling machine to fill up their drinking bottles. The drinking bottles may categorized as X (fill to specification), Y(underfill), and Z (overfill). In general, the underfilling bottle is considered as defective item. Let P(Y)=0.001 while P(X) = 0.990. (i) Find the P(Z). (ii) What is the probability that a drinking bottle does not underfill? (iii) What is the probability that a drinking bottle either overfills or underfills?

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