Problem 1: There are 100 employees at a small college in NS. 57 of the employees are hourly workers, 40 are supervisors, 2 are secretaries, and the remaining employee is the president. Suppose an employee is selected: a. What is the probability the selected employee is an hourly worker? b. What is the probability the selected employee is either an hourly worker or a supervisor? c. Refer to part (b), are these events mutually exclusive? d. What is the probability the selected employee is neither an hourly worker nor a supervisor? Problem 2: Mookie Betts of the Boston Red Sox had the highest batting average for the 2018 Major League baseball season. His average was 0.346. So the likelihood of his getting a hit is 0.346 for each time he bats. Assume he has four times at bat tonight in the red sox-yankee game. a. What type of the probability 0.346 ? b. What is the probability of getting 4 hits in tonight's game? c. Are you assuming his second at bat is independent or mutually exclusive of his first at bat? Explain. d. What is the probability of not getting any hits in the game? e. What is the probability of getting at least one hit? Problem 3 Horwege Electronics inc. purchases TV picture tubes from four different suppliers. Tyson wholesale supplies 20% of the tubes, Fuji importers 30%, Kirkpatricks 25%, and parts inc. 25%. Tyson wholesale tends to have the best quality, as only 3% of its tubes arrive defective. Fuji importers' tubes are 4% defective, Kirkpatrick's 7%, and parts inc.'s are 6.5% defective. a. What is the overall percent defective? b. A defective picture tube was discovered in the latest shipment. What is the probability that it came from Tyson wholesale? Problem 4 The internal revenue service is studying the category of charitable contributions. A sample of 25 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 25 returns, five had charitable contributions of more than $1000. Four of these returns are selected for a comprehensive audit. a. Explain what type of distribution is appropriate to estimate the probability distribution of the four returns and why. b. What is the probability exactly one of the four audited had a charitable deduction of more than $1000 ? c. What is the probability at least one of the audited returns had a charitable contribution of more than $1000