1. Suppose your instructor wants to randomly choose one of the students in the class to ask a question. Suppose the probability that the instructor asks Sam, one of your classmates, is 0.05 and the probability that she/he asks John, another student in your class, is 0.07. What is the probability that the instructor asks one of these two students (assuming independence between these events)? 2. What is wrong with the following statements? Explain your answer. a. The probability that a student misses a class is 0.04 and the probability that he attends the class is 0.9 b. P (A and B) = -0.2 c. P (complement of A) = 0.7 given that P(A) = 0.7 3. Assume 1/3 of UBC students live outside the student housing, 5/9 are originally from BC, and 3/4 are either from BC or live in the student housing. If we randomly choose a student, what is the probability that the student is not from BC and lives in the student housing? 4. The following table shows profit for 150 companies in 4 different industries: Less than or equal to 50 million More than 50 million Total Auto Industry 17 15 32 Steel Industry 35 30 65 Food Industry 28 5 33 Wood Industry 10 10 20 Total 90 60 150 Assume we randomly choose a company, calculate the following probabilities: a. The company has a profit less than or equal to 50 million. b. The company is from the Auto industry. c. The company is from the auto industry and has profit more than 50 million. d. The company is either from the auto company or has a profit more than 50 million. e. The company is from the auto industry given it has profit more than 50 million. f. The company has a profit less than 50 million given it is not from the auto industry. 5. An accountant of an international company is working on a profit-and-loss report for the current fiscal year. The accountant reports that the company incurred a loss in 4 months out of the 12 months in the fiscal year. Let X be the number of months the company is suffering a loss in the next fiscal year. Discuss the adequacy of the model that X follows a binomial distribution with n = 12 and p = 4/12. 6. On average, you receive 3 junk e-mails every 6 hours. Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution. a.What is the expected number of junk e-mails in one day? b.What is the probability of receiving exactly two junk e-mails in a six-hours interval? c.What is the probability of receiving less than two junk e-mails arrive in a six-hours interval? d.What is the probability of receiving two or more junk email in a six-hours interval? 7. A recent survey found that 83% of Canadian were satisfied with their current jobs. Answer the following questions based on a random sample of 10 Canadian workers: a. What is the probability that exactly six employees were satisfied with their current jobs? b. What is the probability that exactly nine employees were satisfied with their current jobs? c. What is the probability that either four or five employees were satisfied with their current jobs? d. What are the mean and standard deviation for this distribution