Simply calling evolution random, with no further explanation, leads many people to believe there has to be another source for "intelligent" evolution, since they think we clearly aren't random.
So you're saying that we should describe evolution not just inaccurately, but contrafactually, because an accurate and factual description will confuse people?
Note this is not the same as the simplification that takes place in General Chemistry and General Physics courses, where rules that are described as true all the time are in fact true only some of the time (e.g., Newtonian mechanics as a simplification and good approximation of relativistic mechanics at non-relativistic speeds). It is an outright fabrication seemingly to protect against a straw man argument of people who don't and more often that not don't want to understand.
Probably the easiest to explain the way the stochastic nature of evolution seems deterministic over evolutionary time is to say, in the general case, over any finite but arbitrarily large number of trials, you (in the impersonal sense) is relatively unlikely to any one result, even the most common one. You are however almost guaranteed of getting a small range of values relative to the range of all possible values. Furthermore, as the range of all possible values increases, the range of "guaranteed" value decreases in relative size. Therefore, as the number of trials goes to infinity, the range of "guaranteed" values converges on one single value, and that is why, over an infinite number of trials, there is a given probability of event happening, while, over a finite number of trials this probability seems to fluctuate.
For instance if your were to toss a fair coin 10,000 times the probability of getting exactly 5,000 heads is .007979, but you can be 95% certain that you will between 4902 and 5098 heads a relative error of 1.96%. Similarly, if you toss a fair coin 1,000,000 times the probability of getting exactly 500,000 heads is .0007979, but you can be 95% certain that you will between 499,020 and 500,980 heads a relative error of .196%. Thus, even though it is not proven here and I myself don't know the exact form of the rigorous mathematical proof, it is reasonable to say that as the number of trial goes to infinity, the probability of getting a head approaches .5, despite the fact that for an arbitrarily large but finite number of trials the probability of getting half head and half tails approaches zero. I will leave others to refine this argument, because in its current form, I don't know how to reselve the apparent contradiction.
The point of that rather lengthy explanation, is that, even though there is random mutation in evolution and natural selection is a stochastic filter, many iterations of these processes cause a convergence in the mean fitness of a population.