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A manufacturing firm employs three analytical plans for the design anmd devel opment of a particular product. For cost reasons, all three are used at varving times. In fact, plans 1, 2, and 3 are used for 30%, 20%, and 50% of the products respectively. The defect rate is different for the three procedures as follows: P(D|P1) = 0.01, P(D|P2) = 0.03, P(D|P3) = 0.02, where P(D|P;) is the probability of a defective product, given plan j. If a random product was observed and found to be defective, which plan was most likely used and thus responsible?

A manufacturing firm employs three analytical plans for the design anmd devel opment of a particular product. For cost reasons, all three are used at varving times. In fact, plans 1, 2, and 3 are used for 30%, 20%, and 50% of the products respectively. The defect rate is different for the three procedures as follows: P(D|P1) = 0.01, P(D|P2) = 0.03, P(D|P3) = 0.02, where P(D|P;) is the probability of a defective product, given plan j. If a random product was observed and found to be defective, which plan was most likely used and thus responsible?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A manufacturing firm employs three analytical plans for the design and devel. opment of a particular product. For cost reasons, all three are used at, varvine times. In fact, plans 1, 2, and 3 are used for 30%, 20%, and 50% of the products respectively. The defect rate is different for the three procedures as follows: P(D|P1) = 0.01, P(D|P2) = 0.03, P(D|P3) = 0.02, %3D where P(D|P;) is the probability of a defective product, given plan j. If a random product was observed and found to be defective, which plan was most likely used and thus responsible?
Transcribed Image Text:A manufacturing firm employs three analytical plans for the design and devel. opment of a particular product. For cost reasons, all three are used at, varvine times. In fact, plans 1, 2, and 3 are used for 30%, 20%, and 50% of the products respectively. The defect rate is different for the three procedures as follows: P(D|P1) = 0.01, P(D|P2) = 0.03, P(D|P3) = 0.02, %3D where P(D|P;) is the probability of a defective product, given plan j. If a random product was observed and found to be defective, which plan was most likely used and thus responsible?
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