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

Question

Quizplus · Accepted Answer

Let's assume that the older machine produces x widgets, so the new machine would produce 3x widgets.

The total number of widgets produced by the company would be 4x.

The number of defective widgets produced by the older machine would be 0.23x, and the number of defective widgets produced by the new machine would be 0.08(3x) = 0.24x.

The total number of defective widgets produced by the company would be 0.23x + 0.24x = 0.47x.

Therefore, the probability of choosing a defective widget would be (0.47x)/(4x) = 0.1175, which is approximately 0.12 or 12%.

Thus, the answer is (B) 0.1175.

A Company Has 2 Machines That Produce Widgets