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.What is the probability that a randomly chosen widget produced by the company is defective?
A) 0.1175
B) 0.078
C) 0.156
D) 0.310

Question

Quizplus · Accepted Answer

The probability of a widget being defective is calculated by taking the weighted average of the defective rates, considering the production volumes of both machines. The older machine's defective rate is 23% (or 0.23), and the new machine's defective rate is 8% (or 0.08). Since the new machine produces three times as many widgets as the older machine, if the older machine produces x widgets, the new machine produces 3x widgets. The total production is x + 3x = 4x widgets. The expected number of defective widgets from the older machine is 0.23x, and from the new machine is 0.08(3x) = 0.24x. The total expected defective widgets are 0.23x + 0.24x = 0.47x. The probability of picking a defective widget is the total expected defective widgets divided by the total production, which is 0.47x / 4x = 0.1175.

A Company Has Two Machines That Produce Widgets