Quality control: A population of 611 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 NonconformingA 81 20B 171 34C 267 38Send data to Excel(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?
Question
Quality control: A population of 611 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 NonconformingA 81 20B 171 34C 267 38Send data to Excel(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?
Solution
(a) The total number of wafers is 611. The number of wafers from Lot C is 267 (conforming) + 38 (nonconforming) = 305. So, the probability that the wafer is from Lot C is 305/611 = 0.4992.
(b) The total number of nonconforming wafers is 20 (from Lot A) + 34 (from Lot B) + 38 (from Lot C) = 92. So, the probability that the wafer is nonconforming is 92/611 = 0.1506.
(c) The number of wafers that are from Lot C and are nonconforming is 38. So, the probability that the wafer is from Lot C and is nonconforming is 38/611 = 0.0622.
(d) Given that the wafer is from Lot C, the total number of wafers to consider is 305. The number of these that are nonconforming is 38. So, the probability that it is nonconforming, given that it is from Lot C, is 38/305 = 0.1246.
(e) Given that the wafer is nonconforming, the total number of wafers to consider is 92. The number of these that are from Lot C is 38. So, the probability that it is from Lot C, given that it is nonconforming, is 38/92 = 0.4130.
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