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[6] A machine is used in a production process. From past data, it is known that 97% of the time the machine is set up correctly. Furthermore, it is known that if the machine is set up correctly, it produces 95% acceptable (non-defective) items. However, when it is set up incorrectly, it produces only 40% acceptable items. a. Show using probabilities that whether the machine produces acceptable items is dependent on whether the machine is set up correctly. b. An item from the production line is selected. What is the probability that the selected item is acceptable? Given that the selected item is acceptable, what is the probability that the machine is set up correctly? C.

[6] A machine is used in a production process. From past data, it is known that 97% of the time the machine is set up correctly. Furthermore, it is known that if the machine is set up correctly, it produces 95% acceptable (non-defective) items. However, when it is set up incorrectly, it produces only 40% acceptable items. a. Show using probabilities that whether the machine produces acceptable items is dependent on whether the machine is set up correctly. b. An item from the production line is selected. What is the probability that the selected item is acceptable? Given that the selected item is acceptable, what is the probability that the machine is set up correctly? C.

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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[6] A machine is used in a production process. From past data, it is known that 97% of the time the machine is set up correctly. Furthermore, it is known that if the machine is set up correctly, it produces 95% acceptable (non-defective) items. However, when it is set up incorrectly, it produces only 40% acceptable items. Show using probabilities that whether the machine produces acceptable items is dependent on whether the machine is set up correctly. а. b. An item from the production line is selected. What is the probability that the selected item is acceptable? Given that the selected item is acceptable, what is the probability that the machine is set up correctly? C.
Transcribed Image Text:[6] A machine is used in a production process. From past data, it is known that 97% of the time the machine is set up correctly. Furthermore, it is known that if the machine is set up correctly, it produces 95% acceptable (non-defective) items. However, when it is set up incorrectly, it produces only 40% acceptable items. Show using probabilities that whether the machine produces acceptable items is dependent on whether the machine is set up correctly. а. b. An item from the production line is selected. What is the probability that the selected item is acceptable? Given that the selected item is acceptable, what is the probability that the machine is set up correctly? C.
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