  We consider discrete optimization problems with interval uncertatinty of
objective function coefficients. The interval uncertainty models measurements
errors. A pos\-sible optimal solution is a solution that is optimal for some
possible values of the coefficients. Pro\-ba\-bi\-li\-ty of a possible solution
is the probability to obtain such coefficients that the solution is optimal.
Similarly we define the notion of a possible approximate solution with given
accuracy and probability of the solution. A possible approximate solution is an
approximate solution that is obtained for some possible values of the
coefficients by some fixed approximate algorithm, e.g. by the greedy algorithm.
Pro\-ba\-bi\-li\-ty of a such solution is the probability to obtain such
coefficients that the algorithm produces the solution as its output. We
consider optimal or approximate possible solution un\-re\-pre\-sen\-ta\-ti\-ve
if its probability less than some boundary value. The mean approximate solution
is a possible approximate solution for midpoints of the coefficients intervals.
The solution may be treated as approximate solution for exact values of the
coefficients. We show that the share of individual discrete optimization
problems instances with unrepresentative mean approximate solution may be wide
enough for rather small values of error and the boundary value. The same is
true for any other possible approximate solution: all of them may be
unrepresentative.
