Practice 1. 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. During this period, line 1, line 2, and line 3 produced 300, 500, and 400 nonconforming cans, respectively. Suppose that one of these 1200 cans is randomly selected. Round to three decimal places. Blemish Crack Pull-Tab Problem Surface Defect Other Total Line 1 Line 2 Line 3 0.15 0.10 0.20 0.40 0.44 0.30 0.31 0.28 0.24 0.10 0.10 0.14 0.04 0.08 0.12 1.00 1.00 1.00 (a) What is the probability that the can was produced by line 3? (b) What is the probability that the reason for nonconformance is a Pull-Tab Problem? (c) Given that the selected can had a Blemish, what is the probability it came from line 1?
Practice 1. 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. During this period, line 1, line 2, and line 3 produced 300, 500, and 400 nonconforming cans, respectively. Suppose that one of these 1200 cans is randomly selected. Round to three decimal places. Blemish Crack Pull-Tab Problem Surface Defect Other Total Line 1 Line 2 Line 3 0.15 0.10 0.20 0.40 0.44 0.30 0.31 0.28 0.24 0.10 0.10 0.14 0.04 0.08 0.12 1.00 1.00 1.00 (a) What is the probability that the can was produced by line 3? (b) What is the probability that the reason for nonconformance is a Pull-Tab Problem? (c) Given that the selected can had a Blemish, what is the probability it came from line 1?
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 82E
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Transcribed Image Text:Practice 1. 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.
During this period, line 1, line 2, and line 3 produced 300, 500, and 400 nonconforming cans,
respectively. Suppose that one of these 1200 cans is randomly selected. Round to three
decimal places.
Blemish
Crack
Pull-Tab Problem
Surface Defect
Other
Total
Line 1 Line 2 Line 3
0.15 0.10
0.20
0.40
0.44
0.30
0.31
0.28
0.24
0.10
0.10
0.14
0.04
0.08
0.12
1.00 1.00
1.00
(a) What is the probability that the can was produced by line 3?
(b) What is the probability that the reason for nonconformance is a Pull-Tab Problem?
(c) Given that the selected can had a Blemish, what is the probability it came from line 1?
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