Answer:
The probability that they will teach different courses is
.
Step-by-step explanation:
Sample space is a set of all possible outcomes of an experiment.
In this case we will write the sample space in the form (x, y).
Here <em>x</em> represents the course taught by the first part-time instructor and <em>y</em> represents the course taught by the second part-time instructor.
Denote every course by their first letter.
The sample space is as follows:
S = {(P, P), (P, I), (P, S), (I, P), (I, I), (I, S), (S, P), (S, I) and (S, S)}
The outcomes where the the instructors will teach different courses are:
s = {(P, I), (P, S), (I, P),(I, S), (S, P) and (S, I)}
The probability of an events <em>E</em> is the ratio of the number of favorable outcomes to the total number of outcomes.
![P(E)=\frac{n(E)}{N}](https://tex.z-dn.net/?f=P%28E%29%3D%5Cfrac%7Bn%28E%29%7D%7BN%7D)
Compute the probability that they will teach different courses as follows:
![P(\text{Different courses})=\frac{n(s)}{n(S)}=\frac{6}{9}=\frac{2}{3}](https://tex.z-dn.net/?f=P%28%5Ctext%7BDifferent%20courses%7D%29%3D%5Cfrac%7Bn%28s%29%7D%7Bn%28S%29%7D%3D%5Cfrac%7B6%7D%7B9%7D%3D%5Cfrac%7B2%7D%7B3%7D)
Thus, the probability that they will teach different courses is
.