Suppose that you are the CEO of a company employing n people. The company has k different ongoing projects and each involves a group of at least r people; note that each individual employee may belong to several project groups. Worried by their lack of basic skills, you decide to send your employees on a training course. There are two different courses offered (Course A and Course B), each covering a different set of skills. You decide that each employee should attend one course, but not both. However, to prevent a project from failing, at least one person in a project group should go to Course A and at least one person should go to Course B. (a) Design a randomized algorithm to assign the employees to the training courses so that the probability for at least one project fails is less than k21-r . Note that you should: i) Present your randomized algorithm idea. ii) Prove that your algorithm satisfies the probability requirement on limiting the failure of the project groups. Hint: refer to the contention resolution example in Section 13.1 (book or slides) (b) If you hope the randomized algorithm result in a at least 34 probability for all k projects to succeed. What is the largest possible number of projects k (represent it in terms of r)?

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Ireally need with these questions.6. what level of job security do athletes and sports competitors have? why do you think this is? 22. do you think a musician has more job security than an athlete? explain.37. what is the difference between a public relations specialist and a marketing professional? 47. do you think gender inequalities still exist in the sports industry? explain.50. what are the advantages and disadvantages of labor unions? do you think labor unions are fair to employers? how might they be taken advantage of?

Exercise 18-15 sheffield appliance center is an experienced home appliance dealer. sheffield appliance center also offers a number of services for the home appliances that it sells. assume that sheffield appliance center sells ovens on a standalone basis. sheffield appliance center also sells installation services and maintenance services for ovens. however, sheffield appliance center does not offer installation or maintenance services to customers who buy ovens from other vendors. pricing for ovens is as follows. oven only $790 oven with installation service 850 oven with maintenance services 970 oven with installation and maintenance services 990 in each instance in which maintenance services are provided, the maintenance service is separately priced within the arrangement at $180. additionally, the incremental amount charged by sheffield appliance center for installation approximates the amount charged by independent third parties. ovens are sold subject to a general right of return. if a customer purchases an oven with installation and/or maintenance services, in the event sheffield appliance center does not complete the service satisfactorily, the customer is only entitled to a refund of the portion of the fee that exceeds $790. assume that a customer purchases an oven with both installation and maintenance services for $990. (b) indicate the amount of revenue that should be allocated to the oven, the installation, and to the maintenance contract.