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) 0.511
B) 0.08
C) 0.15
D) 0.489

Question

Quizplus · Accepted Answer

Using Bayes' theorem, calculate the probability that a defective widget came from the new machine. Let O be the event that a widget is from the older machine, and N be the event that a widget is from the new machine. The probability of a widget being defective given it is from the older machine is P(D|O) = 0.23, and from the new machine is P(D|N) = 0.08. The new machine produces three times as many widgets, so P(N) = 0.75 and P(O) = 0.25. The probability of a widget being defective is P(D) = P(D|O)P(O) + P(D|N)P(N) = 0.23*0.25 + 0.08*0.75 = 0.115. Using Bayes' theorem, P(N|D) = P(D|N)P(N) / P(D) = 0.08*0.75 / 0.115 = 0.511.

A Company Has Two Machines That Produce Widgets