An information technology company produces $42$% of its computer chips at a plant in St. Louis and the remainder of its chips at a plant in Chicago. It is known that $0.85$% of the chips produced in St. Louis are defective, while $0.85$% of the chips produced at the plan in Chicago are defective. What is the probability that a randomly chosen computer chip produced by this company is defective and was produced in St. Louis?