Question 1 (6 points) A headlight produced by Enterprise Lumiere was found to be defective. The company has three factories (labeled below as A, B, and C) where such headlights are manufactured. A Quality Control Manager (QCM) is responsible for investigating the source of found defects, and he had compiled information about the source of possible defects. His research is compiled in the table below. In the cells below, compute the joint probabilies for defective parts from the various factories. Assume that "D" stands for "defective." Compute the marginal probability for defective parts. If a randomly selected headlight is defective, what is the probability that the headlight was manufactured in factory C? Factory % of production Probability of defective A 35% 0.015 B 35% 0.03 C 30% 0.025 P(AD) = P(BD) = P(CD) = P(D) = P(C D) =