A recording company obtains the blank CDs used to produce its labels from three compact disk manufacturers: I, II, and III. The quality control department of the company has determined that 1% of the compact disks produced by manufacturer I are defective, 7% of those produced by manufacturer II are defective, and 3% of those produced by manufacturer III are defective. Manufacturers I, II, and III supply 36%, 20%, and 44%, respectively, of the compact disks used by the company. What is the probability that a randomly selected label produced by the company will contain a defective compact disk?

Answer:3.08%Step-by-step explanation:If we choose a random disk, the probability that it is produced by manufacturer I is 36% so  the probability that it is produced by manufacturer I AND is defective is 1% of 36% Similarly,  the probability that it is produced by manufacturer II is 20% so  the probability that it is produced by manufacturer II AND is defective is 7% of 20% the probability that it is produced by manufacturer III is 44% so  the probability that it is produced by manufacturer III AND is defective is 3% of 44%. Since a disk can only be produced by one manufacturer, the probability that the disk defective is 1% of 36% + 7% of 20% + 3% of 44% = 0.01*0.36 + 0.07*0.20 + 0.03*0.44 = 0.0308 = 3.08%