In a certain electric motor factory, production lines 1, 2, and 3 produce 10%, 40%, and 50%, respectively, of the total output. Of their respective outputs, 5%, 3%, and 1% are defective. An electric motor is selected at random. What is the probability that the motor is defective?

A. 0.022
B. 0.090
C. 0.978

Correct Answer: A

Let A_i denote the event that the motor came from line i, where i = 1, 2, 3, and B denote the event that the motor is defective. Using the total probability rule:
P(B) = P(B|A₁)P(A₁) + P(B|A₂)P(A₂) + P(B|A₃)P(A₃) = 0.05 x 0.10 + 0.03 x 0.40 + 0.01 x 0.50 = 0.022.