A widget dealer purchases 50% of his widgets from factory A, 30% of his widgets from factory B, and.

A widget dealer purchases 50% of his widgets from factory A, 30% of his widgets from

factory B, and 20% of his widgets from factory C. Suppose that the proportion of defective widgets among widgets purchased from factories A, B, and C are .02, .03, and .05,

respectively. (a) What is the probability that a randomly chosen widget from this dealer’s

warehouse is defective? (b) Given that a randomly chosen widget is defective, what are

the probabilities that it came from factory A, factory B, or factory C?