Step 1:

Let $X$ be the random variable denoting the number of marks the student can score while answering 1 question.

The values $X$ can take are 1(for correct answer) or $-\large\frac{1}{2}$(for a wrong answer)

Step 2:

$P(X=1)=\large\frac{1}{4}$ (Since only one out of 4 options is correct)

$P(X=-\large\frac{1}{2})=\frac{3}{4}$

Step 3:

The probability distribution of $X$ is given by

Step 4:

$E(X)=\sum P_i x_i=1\times \large\frac{1}{4}+(-\large\frac{1}{2})\times \large\frac{3}{4}$

$\qquad\qquad\quad\;\;=\large\frac{1}{4}-\frac{3}{8}$

$\qquad\qquad\quad\;\;=\large\frac{-1}{8}$

Step 5:

There are 120 questions in the test.

$\therefore$ expected marks=$120\times -\large\frac{1}{8}=$$-15$