Quality control: A population of

606

semiconductor wafers contains wafers from three lots. The wafers are categorized by lot and by whether they conform to a thickness specification, with the results shown in the following table. A wafer is chosen at random from the population. Write your answer as a fraction or a decimal, rounded to four decimal places.

Lot	Conforming	Nonconforming
A	89	13
B	165	42
C	258	39

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(a) What is the probability that the wafer is from Lot C?

(b) What is the probability that the wafer is nonconforming?

(c) What is the probability that the wafer is from Lot C and is nonconforming?

(d) Given that the wafer is from Lot C, what is the probability that it is nonconforming?

(e) Given that the wafer is nonconforming, what is the probability that it is from Lot C?

(f) Let

E1

be the event that the wafer comes from Lot C, and let

E2

be the event that the wafer is nonconforming. Are

E1

and

E2

independent?