The word "random" has popular connotations which include ideas of "accidental" or at least devoid of conscious choice. The mathematical concept of randomness that we are dealing with here requires the equal probability of selection called for in the basic rule above. For example, popular expression might equate taking a random sample with "interviewing the first ten people I met on the street." But there are issues to consider in determining whether this is a good sample: In what neighborhood did I choose the street? What time of day did I go out? Did I really interview the first ten people or did I fail to count that disreputable looking panhandler? In fact, psychological studies have shown that people are not very good at picking things in a truly random fashion. Biases, conscious and unconscious, creep into the process. By setting up random sampling rules we try to eliminate this kind of human bias.
Researchers who are new to random sampling tend to believe that the accuracy of the sample must depend on what fraction of the population is sampled. In fact, this is not the usual case, and it is only when the sample is quite large, ten percent or more of the population, that the size of the population has anything to do with our calculations. In such cases the program will correct the sample size for the size of the population.
this page is at http://testbed.cis.drexel.edu/sample/whatrandom.html