A factory runs three shifts. The first two shifts produce 500 widgets a week eac

Question

A factory runs three shifts. The first two shifts produce 500 widgets a week each, while the third shift produces 350. Quality control has determined that 10% of the first shift's production is defective, while the second and third shifts have defective rates of 7% and 5% respectively. (a) Interpret this information in terms of conditional probabilities. (b) What is the probability that a randomly selected widget from the factory's overall production will be defective? (c) A randomly selected widget is found to be defective. What is the probability that the widget came from the first shift?

Explanation / Answer

a) probabillity that a widget is defective given from shift A =0.10

probabillity that a widget is defective given from shift B =0.07

probabillity that a widget is defective given from shift C =0.05

b)total number of widgets =500+500+350=1350

therefore probability that a widget is from shift A =(500/1350)

probability that a widget is from shift B =(500/1350)

probability that a widget is from shift C =(350/1350)

therefore probability that a widget is defective =from shift A and defective+from shift B and defective+from shift C and defective =(500/1350)*0.1+(500/1350)*0.07+(350/1350)*0.05 =0.0759

c)probability that widget is defective given came from shift C =(350/1350)*0.05/0.0759 =0.1707

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