  During the Conference on Ulam's Type Stability (Rytro, Poland, 2014), Ioan
Rasa recalled his 25-years-old problem concerning some inequality involving the
Bernstein polynomials. We offer the complete solution (in positive). As a~tool
we use stochastic orderings (which we prove for binomial distributions) as well
as so-called concentration inequality. Our methods allow us to pose (and solve)
the extended version of the problem in question.
