A company has 2 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 3 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

The probability that a defective widget was produced by the new machine can be calculated using Bayes' theorem. 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|O) = 0.23, P(D|N) = 0.08, and P(N) = 3/4, P(O) = 1/4. The probability of a defective widget is P(D) = P(D|O)P(O) + P(D|N)P(N). Using Bayes' theorem, P(N|D) = P(D|N)P(N) / P(D), which calculates to approximately 0.511.

A Company Has 2 Machines That Produce Widgets