Problem 5 (13 marks in total). Personal electronic devices, such as smartphones and tablets are getting more capable all the time. Manufacturing components for these devices is a challenge, and at the same time, consumers are demanding more and more functionality and increasing sturdiness. Microscopic and even submicroscopic flaws can develop during their fabrication that can blank out pixels on the screens or cause intermittent performance failures. Defects will always occur, so the quality engineer in charge of the production process must monitor the number of defects and take action if the process seems out of control. Lets suppose that the engineer is called down to the production line because the number of defects has crossed a threshold. Based on her experience, the engineer thinks there are three possible problems: (1) The motherboards could have faulty connections, (2) the memory could be the source of the faulty connections, or (3) some of the cases may simply be seating incorrectly in the assembly line. She knows from past empirical data how often these types of problems crop up and how likely it is that just making an adjustment will fix each type of problem. Motherboard issues are rare (10%), memory problems have been showing up about 30% of the time, and case alignment issues occur most often (60%). In addition, past data indicate that 10% of the motherboard problems have been fixed versus 50%, and 80% for memory and case alignment issues, respectively. (a) (5 marks) Draw the probability tree associated with this problem (indicating the associated probabilities on the branches). (b) (3 marks) Whats the probability that the problem will be fixed by a simple adjustment? (c) (5 marks) Lets assume that the problem is fixed, was it more likely to be a case alignment issue or a motherboard issue?