A company has two machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces three times as many widgets as the older machine does. Given a randomly chosen widget was tested and found to be defective, what is the probability it was produced by the new machine?
A) 0.08
B) 0.15
C) 0.489
D) 0.511

Question

Quizplus · Accepted Answer

Using Bayes' theorem, we calculate the probability that a defective widget was produced by the new machine. Let O be the event that a widget is produced by the older machine and N be the event that a widget is produced by the new machine. We have P(D|N) = 0.08, P(D|O) = 0.23, P(N) = 0.75, and P(O) = 0.25. The probability of a defective widget, P(D), is P(D|N)P(N) + P(D|O)P(O) = 0.08*0.75 + 0.23*0.25 = 0.12. Using Bayes' theorem, P(N|D) = P(D|N)P(N) / P(D) = 0.08*0.75 / 0.12 = 0.511.

A Company Has Two Machines That Produce Widgets