Hello there. To solve this question, we need to remember some properties on probabilities.
To find the probability of choosing a professor or an instructor from the members of the mathematics faculty, first we need to sum the number of members to get the total number of people (also called sample)
So, if we have 5 professors, 6 assistant professors, 6 associate professors and 6 instructors, we have a total of 23 persons.
Now, remember the probability for an event occur is calculated by the ratio of the favorable events of occurring what we want and the sample space.
So, considering professors is not equal to assistant professors and also not equal to associate professors, we need to sum the probabilites of getting a professor and also the probability of getting an instructor.
The probability of getting a professor is equal to:
professor/sample = 5/23
The probability of getting an instructor:
instructor/sample = 6/23
Sum these values:
5/23 + 6/23 = 11/23
This is the probability we were looking for.