Q1) At large urban university there are only 10 times in the week which a class or section can be planned (this permits time for faculty naps, cat-feeding, and so on).  University utilizes undergraduate TAs for its Principles of Economics courses. Sequence works like this.  First university (randomly) chooses a time when discussion section will be held.  Then it assigns TAs to course, which then select discussions they will lead.  Problems take place as undergraduate TAs already have their class schedules when they find out which class they will be allotted to.  Each undergraduate TA takes five courses, additionally to working as TA, and so there are five times a week when she cannot lead a discussion section. Undergraduate TAs also selects their classes arbitrarily.

University needs that there be one TA for every 50 students.  All semester 100 students wish to take Principles of Economics.  There are 2 methods the 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.  Former is called "small classes;" the latter, "big class." (Faculty "work" for free.)

1) Determine the probability in big class that both sections are covered? Only one section? Neither section?  Determine the expected number of sections covered?

2) Determine the probability that big class arrangement covers more sections than small classes arrangement?  Describe why using 4 x 4 table