From past experience it is known that a machine is set up correctly on 80% of the occasions.  If the machine is set up correctly then 85% of the good parts are expected but if the machine is not correctly set up then the probability of a good part is only 30%. On a particular day the machine is set up and the 1st component produced was found to be good.  What is the probability that the machine is correctly set up?

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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From past experience it is known that a machine is set up correctly on 80% of the occasions.  If the machine is set up correctly then 85% of the good parts are expected but if the machine is not correctly set up then the probability of a good part is only 30%. On a particular day the machine is set up and the 1st component produced was found to be good.  What is the probability that the machine is correctly set up?

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