http://evolution.berkeley.edu/evosite/evo101/IIIC1aRandom.shtml
(experiments have made it clear that many mutations are in fact "random," and did not occur because the organism was placed in a situation where the mutation would be useful. For example, if you expose bacteria to an antibiotic, you will likely observe an increased prevalence of antibiotic resistance.)
&
http://evolution.berkeley.edu/evosite/evo101/IIIC1bLederberg.shtml
(The hypothesis for the experiment is that antibiotic resistant strains of bacteria surviving an application of antibiotics had the resistance before their exposure to the antibiotics, not as a result of the exposure.)

uses the term 'random' merely to demonstrate contrast to 'directed' mutations - 'did not evolve resistance in response to exposure to the antibiotic' which would have been a 'directed' mutation. Here, random merely means - no control exercised in the context of the exposure to antibiotics, by the case of the exposure itself.

This of course is merely using the same 'word' to have a different semantic content in a different field to the semantic content used in Mathematics.

We really need blatantly obvious 'semantic signals' to stop the untrained (one could also say 'layman') from just grabbing all the semantic baggage of a 'word' from one field and dragging into another unrelated field where it creates unnecessary and unwanted obfuscation.

FSM Rules!