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A machine is used in a production process. From past data, it is known that 97%...

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. An item from the production line is selected. What is the probability that the selected item is non-defective?
b. Given that the selected item is non-defective, what is the probability that the machine is set up correctly?
Math   Statistics-And-Probability   
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