Write an optional reasoning for your answer: c) (20 points) Suppose that Harry does not remember the condition of his teeth exactly. However, he thinks that his teeth did not required any work w.p. 0.4, cleaning required w.p. 0.15, and filling required w.p. 0.45. What is the probability that no work will be required in his visit to the dentist two years from now? Write an optional reasoning for your answer: d) (10 points) Calculate the probability that Harry's teeth will not require any work in his next two visits to the dentist. Write an optional reasoning for your answer: e) (15 points) What is the average number consecutive visits to the visits to the dentist's office that Harry's teeth will not require any work? Explain the meaning of the value you find briefly. Write a required reasoning for your answer: Write an optional reasoning for your answer: c) (20 points) Suppose that Harry does not remember the condition of his teeth exactly. However, he thinks that his teeth did not required any work w.p. 0.4, cleaning required w.p. 0.15, and filling required w.p. 0.45. What is the probability that no work will be required in his visit to the dentist two years from now? Write an optional reasoning for your answer: d) (10 points) Calculate the probability that Harry's teeth will not require any work in his next two visits to the dentist. Write an optional reasoning for your answer: e) (15 points) What is the average number consecutive visits to the visits to the dentist's office that Harry's teeth will not require any work? Explain the meaning of the value you find briefly. Write a required reasoning for your answer: Question 2 (85 points) Harry visits the dentist every six months (i.e., time between two visits is 6 months). Because of a sweet tooth, the condition of his teeth varies among three possible conditions: No work is required (1), cleaning is required (2), and filling is required (3). If no work is required in Harry's most recent visit to the dentist, w.p. 0.4 a cleaning will be required, w.p. 0.3 a filling will be required. If cleaning is required in Harry's most recent visit to the dentist, w.p. 0.4 no work will be required and, w.p. 0.2 a filling will be required. If filling is required in Harry's most recent visit to the dentist, w.p. 0.6 no work will be required, w.p. 0.2 a cleaning will be required. Do NOT enter any units into the boxes. Just enter a number as 0.111 or 11.235 with three digit precision. a) (20 points) Suppose that in Harry's last visit to the dentist no work was required. Calculate the probability that no work will be required in his next visit and filling will be required in the following two visits after that. Write an optional reasoning for your answer: b) (20 points) Suppose that in his last visit Harry got his teeth cleaned, what is the probability that his teeth will require no work after 3 visits. Write an optional reasoning for your answer: c) (20 points) Suppose that Harry does not remember the condition of his teeth exactly. However, he thinks that his teeth did not required any work w.p. 0.4, cleaning required w.p. 0.15, and filling required w.p. 0.45. What is the probability that no work will be required in his visit to the dentist two years from now