  The expected number of zeros of a random real polynomial of degree $N$
asymptotically equals $\frac{2}{\pi}\log N$. On the other hand, the average
fraction of real zeros of a random trigonometric polynomial of increasing
degree $N$ converges to not $0$ but to $1/\sqrt 3$. An average number of roots
of a system of random trigonometric polynomials in several variables is equal
to the mixed volume of some ellipsoids depending on the degrees of polynomials.
Comparing this formula with Theorem BKK we prove that the phenomenon of nonzero
fraction of real roots remains valid.
