Question

A large Computer Company A, subcontract the manufacturing of its circuit board 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 boards are completed by companies D,E and C , they are shipped to Company A to be used in various computer models. It has been found that 1.5% , 1% and 0.5% of the boards from D,E and C respectively prove defection during the 90 day warranty period after a computer is first sold. What is the probability that a given board will be defective during the 90 day period?