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

Using Bayes' theorem, calculate the probability that a defective widget came from the new machine. The probability of a widget being defective from the new machine is 0.08, and the new machine produces 3 times as many widgets as the old one. The combined probability of a widget being defective is calculated, and then the probability that a defective widget is from the new machine is found to be approximately 0.511.

A Company Has 2 Machines That Produce Widgets