A factory has two production lines A and B, production line A works 7 days a week, production line B works only 5 days a week. Production line A produces 5000 items each day where 80% of the produced items are high quality and the rest are of medium quality. Production line B produces 3500 items each day where 62% of the produced items are high quality, 15% medium quality, and the rest are of low quality. All items produced after working for many weeks are accumulated in a warehouse. If an item is tested and found to be of medium quality, what is the probability that it was produced by production line B. [The answer should be a number rounded to five decimal places, don't use symbols such

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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A factory has two production lines A and B,
production line A works 7 days a week,
production line B works only 5 days a week.
Production line A produces 5000 items each
day where 80% of the produced items are
high quality and the rest are of medium
quality. Production line B produces 3500
items each day where 62% of the produced
items are high quality, 15% medium quality,
and the rest are of low quality. All items
produced after working for many weeks are
accumulated in a warehouse.
If an item is tested and found to be of
medium quality, what is the probability that it
was produced by production line B.
(The answer should be a number rounded to
five decimal places, don't use symbols such
Transcribed Image Text:A factory has two production lines A and B, production line A works 7 days a week, production line B works only 5 days a week. Production line A produces 5000 items each day where 80% of the produced items are high quality and the rest are of medium quality. Production line B produces 3500 items each day where 62% of the produced items are high quality, 15% medium quality, and the rest are of low quality. All items produced after working for many weeks are accumulated in a warehouse. If an item is tested and found to be of medium quality, what is the probability that it was produced by production line B. (The answer should be a number rounded to five decimal places, don't use symbols such
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