The probability that a student does not own a car is \(1 - \frac{1}{4} = \frac{3}{4} = 0.75\).

The probability that none of the \(n\) students owns a car is \(0.75^n\).

We need the probability that at least one student owns a car to be greater than 0.995:

\(1 - 0.75^n > 0.995\)

\(0.75^n < 0.005\)

Taking logarithms on both sides:

\(n \log(0.75) < \log(0.005)\)

\(n > \frac{\log(0.005)}{\log(0.75)}\)

Calculating the right-hand side gives \(n > 18.4\).

Therefore, the least possible integer value of \(n\) is 19.