Two part-time teachers are hired by the mathematics department and each teacher

Question

Two part-time teachers are hired by the mathematics department and each teacher is randomly assigned to teach one course: either Trigonometry, Algebra I, or Calculus I. (a) Both part-time teachers can be assigned to teach the same course, and so the resulting sample space is: {(a, t), (a, c), (a, a), (c, t), (c, c), (c, a), (t, t), (t, c), (t, a)} Notice that (a, t) and (t, a) are listed as different outcomes in the sample space. Explain why order matters in this case. (b) Find the probability that they will both teach Calculus I. (c) Both of the part-time teachers are assigned to teach Calculus I. Some of the full-time teachers are upset, because they believe the selection was not random, and that the part-timers were given preferential treatment. Do you think the full-time instructors have a valid argument? Why or why not?

Explanation / Answer

a. In this case order matters because the event is completely different when teacher one gets one subject and second teacher teaches another, it is not the same situation. Therefore, the order matters.

b. The total number of outcomes in the sample space is 9

In only one case both teachers get calculus

so, the probabilty is 1/9.

c. The probablity of each outcome is 1/9 according to the given sample space. Therefore,it cannot be an unfair selection. Teachers could have been assigned any subjects, each outcome has the same probabibility. Therefore, the argument is not valid.

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