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 90% of the produced items are high quality and the rest are of medium quality. Production line B produces 3500 items each day where 63% of the produced items are high quality, 19% 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 A. [The answer should be a number rounded to five decimal places, don't use symbols such as %)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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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 90% of the produced items are high quality
and the rest are of medium quality. Production
line B produces 3500 items each day where 63%
of the produced items are high quality, 19%
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 A.
[The
answer should be a number rounded to five
decimal places, don't use symbols such as %]
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 90% of the produced items are high quality and the rest are of medium quality. Production line B produces 3500 items each day where 63% of the produced items are high quality, 19% 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 A. [The answer should be a number rounded to five decimal places, don't use symbols such as %]
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