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) 0.156
C) 0.1175
D) 0.310

Question

Quizplus · Accepted Answer

Let's assume that the company produces 100 widgets in total, with the older machine producing 40 widgets and the new machine producing 60 widgets. We can then calculate the total number of defective widgets produced by each machine:

Older machine: 0.23 x 40 = 9.2 defective widgets
New machine: 0.08 x 60 = 4.8 defective widgets

The total number of defective widgets produced by the company is the sum of the defective widgets produced by each machine:

Total defective widgets: 9.2 + 4.8 = 14

Therefore, the probability of selecting a defective widget from the company's production is:

P(defective) = 14/100 = 0.14

Answer C (0.1175) is the closest option to our calculation (0.14) and is therefore the best choice.

A Company Has 2 Machines That Produce Widgets