This problem involves a binomial distribution, which is applicable when a student guesses randomly on a multiple-choice test. The parameters for a binomial distribution are:

• $n$ = the number of trials (questions)
• $p$ = the probability of success on each trial (answering a question correctly)
• $X$ = the number of questions answered correctly

For this case:

• Each question has 4 choices, so the probability of guessing correctly is $p = \frac{1}{4} = 0.25$.
• The number of trials $n$ is the total number of questions.
• We are asked to find $P(X = 4)$, the probability that the student answers exactly 4 questions correctly.

The probability mass function for a binomial distribution is:

$P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}$

Where:

• $\binom{n}{k}$ is the binomial coefficient, representing the number of ways to choose $k$ successes (correct answers) out of $n$ trials (questions).
• $p$ is the probability of success.
• $k$ is the number of correct answers we are calculating the probability for.

To provide a concrete answer, I need the total number of questions $n$. Could you provide that detail?