Let \(X\) be the number of students who own a car out of the five chosen. \(X\) follows a binomial distribution with parameters \(n = 5\) and \(p = \frac{1}{4}\).

We need to find \(P(X \geq 4) = P(X = 4) + P(X = 5)\).

Using the binomial probability formula:

\(P(X = 4) = \binom{5}{4} \left( \frac{1}{4} \right)^4 \left( \frac{3}{4} \right)^1\)

\(P(X = 5) = \binom{5}{5} \left( \frac{1}{4} \right)^5 \left( \frac{3}{4} \right)^0\)

Calculating each term:

\(P(X = 4) = 5 \times \left( \frac{1}{4} \right)^4 \times \frac{3}{4} = 0.014648\)

\(P(X = 5) = 1 \times \left( \frac{1}{4} \right)^5 = 0.00097656\)

Adding these probabilities gives:

\(P(X \geq 4) = 0.014648 + 0.00097656 = 0.0156\)

Thus, the probability that at least four of these students own a car is \(0.0156\) or \(\frac{1}{64}\).