Most cubic polynomials with real coefficients have two turning points, a local maximum and a local minimum. But how do you quantify “most”?
Here’s how one author did it . Start with the cubic polynomial
x³ + ax² + bx + c
Since multiplying a polynomial by a nonzero constant doesn’t change how many turning points it has, we might as well assume the leading coefficient is 1.
In his paper, Robert Fakler assumes a, b, and c are chosen randomly from an interval [-k, k]. He shows that for k ≤ 3, the probability that the polynomial has two turning points is
p = (9 + k)/18.
For k ≥ 3, the probability is
p = 1 – √(3/k) / 3
and so as k → ∞, p → 1.
 Robert Fakler. Do Most Cubic Graphs Have Two Turning Points? The College Mathematics Journal, Vol. 30, No. 5 (Nov., 1999), pp. 367-369