An automobile manufacturer obtains the microprocessor used to regulate fuel consumption in its automobiles from three microelectronic firms: A, B, and C. The quality-control department of the company has determined that 2% of the microprocessors produced by firm A are defective, 1.5% of those produced by firm B are defective, and 3% of those produced by the firm C are defective. Firms A, B, and C supply 40%, 30%, and 30%, respectively, of the microprocessors used by the company. What is the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor?

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor, we need to find the weighted average of the probability of a defective microprocessor from each of the three firms, using their respective market share as weights. 
P(defective) = (0.02 x 0.40) + (0.015 x 0.30) + (0.03 x 0.30) 
P(defective) = 0.008 + 0.0045 + 0.009 
P(defective) = 0.0215 
Therefore, the probability of a randomly selected automobile manufactured by the company having a defective microprocessor is 0.0215 or 2.15%. The answer is option C.

An Automobile Manufacturer Obtains the Microprocessor Used to Regulate Fuel