In Example 5, what is the probability that a given onboard computer came from company E or C?

Data from Example 5

An auto company A subcontracts the manufacturing of its onboard computers to two companies: 40% to company B and 60% to company C. Company B in turn subcontracts 70% of the orders it receives from company A to company D and the remaining 30% to company E, both subsidiaries of company B. When the onboard computers are completed by companies D, E, and C, they are shipped to company A to be used in various car models. It has been found that 1.5%, 1%, and .5% of the boards from D, E, and C, respectively, prove defective during the 3-year warranty period after a car is first sold. What is the probability that a given onboard computer will be defective during the 3-year warranty period?