At the large urban university there're only ten times throughout the week that a class or section can be scheduled (this allows time for faculty naps, cat-feeding, and so forth). The university employs undergraduate TAs for its Principles of Economics courses. The sequence works like this. First university (randomly) picks time when discussion section will be held. Then it assigns TAs to the course, who then choose the discussions they will lead. Problems arise since undergraduate TAs already have their class schedules when they learn which class they will be allocated to. Each undergraduate TA takes five courses, in addition to working as TA, and so there're five times a week when she can't lead the discussion section. Undergraduate TAs also select their classes randomly.
The university requires that there be one TA for every 50 students. Every semester 100 students want to take Principles of Economics. There're two ways Economics Department can arrange this. They can schedule two separate classes of 50, each with its own TA and discussion section time, or one class of 100 with two TAs. The former is named as "small classes;" the latter, "big class." (Faculty "work" for free.)
1. Assume instead that the Department schedules one class of 100 (big class. Call the two discussion sections A and B. Consider the particular TA assigned to this course. Find out the probability which she can cover either section? Neither section? Section A but not section B? Section B but not section A?.
2. Recommend both TAs and construct a 4 x4 table of possible outcomes in terms of above let one TA be vertical and other horizontal. Find out the probability of each cell in table? For what cells are both sections covered? Only one section covered? Both sections covered?