Romi, a production manager, is trying to improve the efficiency of his assembly line. He knows that the machine is set up correctly only 60% of the time. He also knows that if the machine is set up correctly, it will produce good parts 80% of the time, but if set up incorrectly, it will produce good parts only 20% 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. What is the revised probability that the machine was set up correctly?
A) 48%
B) 56%
C) 86%
D) 96%

Question

Quizplus · Accepted Answer

Using Bayes' theorem:
P(set up correctly | first part is good) = P(first part is good | set up correctly) * P(set up correctly) / P(first part is good)
P(first part is good) = [P(first part is good | set up correctly) * P(set up correctly)] + [P(first part is good | set up incorrectly) * P(set up incorrectly)]
= (0.8*0.6) + (0.2*0.4) = 0.56
P(set up correctly | first part is good) = (0.8 * 0.6) / 0.56 = 0.8571 or 86% (rounded to nearest whole number)

Romi, a Production Manager, Is Trying to Improve the Efficiency