Suppose the probability that the instructor asks Sam, one of your classmates, is 0.05 and the probability that he/he asks John, another student in your class, is 0.07. What is the probability that the instructor asks one of hese 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. A company has 750 employees. 450 of the employees are females. Half the female are less than thirty years old, and one-fourth of the male workers are less than thirty years old. If one of the workers of the company is selected at random to receive a prize, what is the probability that the person selected is less than thirty years old? 4. The following table shows profit for 150 companies in 4 different industries: Less than or equal to 50 More than 50 million Total million 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. . An accountant of an international company is working on a profit-and-loss report for the current fiscal year. The ccountant 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 hat X follows a binomial distribution with n = 12 and p = 4/12. 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. What is the expected number of junk e-mails in one day