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18. Apple sells two models of iPhone 7: the 4.7-inch model and the 5.5-inch Plus model. Sincelast September, 75% of the sold iPhone 7’s were the 4.7-inch model and 25% were the 5.5-inch Plus model. Of those customers who bought the 4.7-inch iPhone 7, 45% purchased anAppleCare extended warranty; whereas 65% of all 5.5-inch iPhone 7 Plus buyers purchasedan AppleCare extended warranty. What is the probability that the next iPhone 7 buyer willpurchase an AppleCare extended warranty? (Hint: use the law of total probability.)a. 0.45b. 0.50c. 0.55d. 0.6019. Continuing the last question, if the next buyer is known to have purchased an AppleCareextended warranty, how likely is it that he or she has bought the 4.7-inch iPhone 7 model?(Hint: use Bayes’ Theorem.)4
123420. The above figure shows a system that consists of four components. Because components 1 and2 are connected in parallel, the subsystem (1-2) works if at least one of the two componentsworks. Similarly, components 3 and 4 are connected in parallel in the subsystem (3-4), whosefunctioning thus requires that one or both of components 3 and 4 work. The two subsystems,(1-2) and (3-4), are connected in series; therefore, both subsystems must work for the wholesystem to work.Suppose the components work independently of one another, and eachcomponent works with probability 0.8. What is the probability that the whole system works?5