The introduction of product randomness helps us make sense of some familiar uses of ‘random’ to characterise an entire collection of outcomes of a given repeated process. This is the sense in which a random sample is random: it is an unbiased representation of the population from which it is drawn—and that is a property of the entire sample, not each individual member. If a random sample is to do its job, it should be irregular and haphazard with respect to the population variables of interest. We should not be able to predict the membership of the sample to any degree of reliability by making use of some other feature of individuals in the population. (So we should not be able to guess at the likely membership of a random sample by using some feature like ‘is over 180cm tall’.) A random sample is one that is representative in the sense of being typical of the underlying population from which it is drawn, which means in turn that—in the ideal case—it will exhibit no order or pattern that is not exemplified in that underlying population.