Random is not a coin toss. With enough information, including the size of the coin, the amount of force in the toss, the local atmosphere, which side starts up, and a big enough computer, its likely you can better your odds from 50/50.
In research a random sample is critical, and always a source of critical pleasure for the irate reviewer. What does random mean? It means that every individual (be it organism, gene, or aliquot) in the population from which you are sampling has an equal chance of being selected. Uh.. come again? what does that mean?
So what is a population. In ecology it means something different from stats. In ecology it is a local group of organisms. In data analysis is the hypothetical, unknowable, infinite set of all possible things that you are interested in. So, you are curing cancer, your population includes not just everyone right now who meets your criteria, but also all the people who will get cancer in the future who might be helped by your cure. Well, that pretty much blows the concept of random out of water or the room or whatever.
The sample is what you take from the population. Every member of your sample comes from your population, whether you are doing molecular genetics and extracting Dr. O. Sophila’s DNA or population genetics and taking his offspring. Usually, as we are happy with a coin toss, we are not so worried that we are not sampling individuals in the future. But what constitutes random sampling is a real problem. Bias, increasing the probability that some members are more likely to be selected than others, can be, but doesn’t have to be, a problem.
When is not a problem? When you can demonstrate (ah-ha, tricky) that the bias in your sample has nothing to do with the question at hand. Simple example: if you are studying wasp stinger length and wasps come in two colors, red and gold. If you can show that color is not correlate with length, then the fact that you get more reds than golds isn’t a problem.