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) 0.511
B) 0.489
C) 0.15
D) 0.08

Question

Quizplus · Accepted Answer

Using Bayes' theorem, the probability that a defective widget was produced by the new machine is calculated as follows: P(New | Defective) = [P(Defective | New) * P(New)] / P(Defective). Here, P(Defective | New) = 0.08, P(New) = 3/4 (since the new machine produces 3 times as many widgets), and P(Defective) = 0.08*(3/4) + 0.23*(1/4). Solving gives approximately 0.511.

A Company Has 2 Machines That Produce Widgets