Quality control: A population of 597 semiconductor wafers contains wafers from three lots. The wafers are categorized by lot and

Question

Quality control: A population of 597 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 21
B 159 40
C 253 35
(a) What is the probability that the wafer is from Lot A?
(b) What is the probability that the wafer is conforming?
(c) What is the probability that the wafer is from Lot A and is conforming?
(d) Given that the wafer is from Lot A, what is the probability that it is conforming?
(e) Given that the wafer is conforming, what is the probability that it is from Lot A?
(f) Let E₁ be the event that the wafer comes from Lot A, and let E₂ be the event that the wafer is conforming. Are E1 and E₂ independent?

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