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)?