SOLUTION: A previous survey shows that a machine making plastic components is correctly set up for the day's production on 95% of days. On days when it is set up correctly, 98% of the compon

Question 1102486: A previous survey shows that a machine making plastic components is correctly set up for the day's production on 95% of days. On days when it is set up correctly, 98% of the components produced are good. If the machine is not set up correctly, only 40% of the components produced are good. On a particular day, the machine is set up and the first component produced is found to be good. What is the probability that the machine is set up correctly?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
P(MG|PGood)=P(PGood|MG)*P(MG)/P(Part good|MG)*P(MG)+P(Part good)|MN)*P(MN)
This is 0.98*0.95/(0.98*0.95)+(0.4)*(0.05)=0.931/0.953=0.977 or 97.7%
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