Calculation:

Consider the total number of students in the class to be 128.

Therefore, \(\displaystyle{n}{\left({S}\right)}={128}\).

Compute the number of students who are on the honor roll and not going to college.

\(\displaystyle{56}-{48}={4}\)

Compute the number of students who are not on the honor roll and not going to college.

\(\displaystyle{76}-{56}={20}\)

Compute the total number of students not going to college.

\(\displaystyle{n}{\left({E}\right)}={4}+{20}={24}\)

Compute the probability of event E by dividing the number of outcomes of an event by the number of outcomes of sample space.

\(\displaystyle{P}{\left({E}\right)}={\frac{{{n}{\left({E}\right)}}}{{{n}{\left({S}\right)}}}}\)

\(\displaystyle={\frac{{{24}}}{{{128}}}}\)

\(\displaystyle={\frac{{{3}}}{{{16}}}}\)

Therefore, the probability that a student is not going to college is \(\displaystyle{\frac{{{3}}}{{{16}}}}\).

Consider the total number of students in the class to be 128.

Therefore, \(\displaystyle{n}{\left({S}\right)}={128}\).

Compute the number of students who are on the honor roll and not going to college.

\(\displaystyle{56}-{48}={4}\)

Compute the number of students who are not on the honor roll and not going to college.

\(\displaystyle{76}-{56}={20}\)

Compute the total number of students not going to college.

\(\displaystyle{n}{\left({E}\right)}={4}+{20}={24}\)

Compute the probability of event E by dividing the number of outcomes of an event by the number of outcomes of sample space.

\(\displaystyle{P}{\left({E}\right)}={\frac{{{n}{\left({E}\right)}}}{{{n}{\left({S}\right)}}}}\)

\(\displaystyle={\frac{{{24}}}{{{128}}}}\)

\(\displaystyle={\frac{{{3}}}{{{16}}}}\)

Therefore, the probability that a student is not going to college is \(\displaystyle{\frac{{{3}}}{{{16}}}}\).