Romi, a production manager, is trying to improve the efficiency of his assembly line. He knows that the machine is set up correctly only 70% of the time. He also knows that if the machine is set up correctly, it will produce good parts 95% of the time, but if set up incorrectly, it will produce good parts only 40% of the time. Romi starts the machine and produces one part before he begins the production run. He finds the first part to be good. Using Bayes theorem, what is the revised probability that the machine was set up correctly?

0.8471

Step-by-step explanation:

Using BAYES THEOREM:

P(correct setup) = 0.7

P(correct setup^c) = 1 - 0.7 = 0.3

P(good part | correct setup) = 0.95

P(good part | Incorrect setup) = 0.4

Probability that a good part is produced :

[P(correct setup) * P(good part | correct setup)] + [P(incorrect setup) * P(good part | Incorrect setup)]

= (0.7 * 0.95) + (0.3 * 0.4) = 0.785

Probability that machine was setup correctly, when he finds the first part to be good :

[P(correct setup) * P(good part | correct setup)] / P(A good part is produced)

= (0.7 * 0.95) / 0.785

= 0.665 / 0.785

= 0.8471