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Blemish Crack Pull-Tab Problem Surface Defect Other 15 50 21 10 4 12 44 28 8 8 20 40 24 15 2 During this period, line 1 produced 500 nonconforming cans, line 2 produced 200 such cans, and line 3 was responsible for 800 nonconforming cans. Suppose that one of these 1,500 cans is randomly selected. (a) What is the probability that the can was produced by line 1? (Round your answer to three decimal places.) What is the probability that the reason for nonconformance is a crack? (Round your answer to three decimal places.) (b) If the selected can came from line 1, what is the probability that it had a blemish? (c) Given that the selected can had a surface defect, what is the probability that it came from line 1? (Round your answer to three decimal places.)

Blemish Crack Pull-Tab Problem Surface Defect Other 15 50 21 10 4 12 44 28 8 8 20 40 24 15 2 During this period, line 1 produced 500 nonconforming cans, line 2 produced 200 such cans, and line 3 was responsible for 800 nonconforming cans. Suppose that one of these 1,500 cans is randomly selected. (a) What is the probability that the can was produced by line 1? (Round your answer to three decimal places.) What is the probability that the reason for nonconformance is a crack? (Round your answer to three decimal places.) (b) If the selected can came from line 1, what is the probability that it had a blemish? (c) Given that the selected can had a surface defect, what is the probability that it came from line 1? (Round your answer to three decimal places.)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 80E
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A factory uses three production lines to manufacture cans of a certain type. The accompanying table gives percentages of nonconforming cans, categorized by type of nonconformance, for each of the three lines during a particular time period. Blemish Crack Pull-Tab Problem Surface Defect Other Line 1 Line 2 Line 3 15 12 20 50 44 40 21 28 24 10 8 15 4 8 2 During this period, line 1 produced 500 nonconforming cans, line 2 produced 200 such cans, and line 3 was responsible for 800 nonconforming cans. Suppose that one of these 1,500 cans is randomly selected. (a) What is the probability that the can was produced by line 1? (Round your answer to three decimal places.) What is the probability that the reason for nonconformance is a crack? (Round your answer to three decimal places.) (b) If the selected can came from line 1, what is the probability that it had a blemish? (c) Given that the selected can had a surface defect, what is the probability that it came from line 1? (Round your answer to three decimal places.)
Transcribed Image Text:A factory uses three production lines to manufacture cans of a certain type. The accompanying table gives percentages of nonconforming cans, categorized by type of nonconformance, for each of the three lines during a particular time period. Blemish Crack Pull-Tab Problem Surface Defect Other Line 1 Line 2 Line 3 15 12 20 50 44 40 21 28 24 10 8 15 4 8 2 During this period, line 1 produced 500 nonconforming cans, line 2 produced 200 such cans, and line 3 was responsible for 800 nonconforming cans. Suppose that one of these 1,500 cans is randomly selected. (a) What is the probability that the can was produced by line 1? (Round your answer to three decimal places.) What is the probability that the reason for nonconformance is a crack? (Round your answer to three decimal places.) (b) If the selected can came from line 1, what is the probability that it had a blemish? (c) Given that the selected can had a surface defect, what is the probability that it came from line 1? (Round your answer to three decimal places.)
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