A mathematics faculty have:
4 Professors (P)
4 Associate professors (AP)
9 Assistant professors (ASP)
6 Instructors (I)
Total= 23
Probability is represented by the following expression:
[tex]P(A)=\frac{\text{Number of favourable outcomes}}{\text{Total number of favourable outcomes}}[/tex]So, the probability of choosing a professor:
[tex]P(P)=\frac{4}{23}[/tex]The probability of choosing an instructor:
[tex]P(I)=\frac{6}{23}[/tex]Then, the probability of choosing a professor or an instructor would be the addition of P(P) and P(I):
[tex]\begin{gathered} P(P\text{ or I)=P(P)+P(I)} \\ P(P\text{ or I)=}\frac{4+6}{23}=\frac{10}{23} \end{gathered}[/tex]