As you flip a coin into infinity (at least hundreds of times), you will come increasingly closer to a bell curve (a normal distribution). That means you will approximate 50% heads and 50% tails (though you will never actually achieve it).

In this exercise, the population, or sampling universe (where the sample is drawn from), consists of one head and one tail. The simple random sample (where each member of the sampling universe has an equal chance of being included in the sample) is the total number of flips.

Moreover, as is the case with all random samples, neither the one(s) taking the sample nor the members of the sampling universe have any control of who (or what) is ultimately included in the sample. If either type of manipulation exists in the sampling process, the sample is, by definition, accidental (i.e., nonscientific).

If ten consecutive flips result in ten tails, one cannot reliably predict that the next flip is more likely to produce a head (or a tail for that matter). Statistics does not work that way. Each flip of the coin is entirely independent, and the probability of getting a head or a tail remains constant at 50% for each flip.

This JavaScript program (below) is a simple coin flipper. To begin, simply click on the Flip Coin button.

Here is a JavaScript program which will allow you to extract a simple random sample (where every member of the population has an equal chance of being included in the sample), not simply to perform a coin-flipping demonstration. It is much more sophisticated:

The randomization widget below comes courtesy of the Research Randomizer site:

If anyone is interested in more of the philosophical aspects of this subject, please read on:

Free will is individual. Determinism is collective.

Statistically, I can predict the behavior of a category of people but not of a single individual in that category. For instance, I can say that males under 25 have a higher rate of auto accidents than males over 25. However, if I then claim that because you are under 25, and I am over 25, that you are more likely to have an auto accident than me, then I am committing the ecological fallacy, i.e., making inferences about individual behavior based on aggregate demographic data.

The danger of psychologism is the opposite of the ecological fallacy, the individual fallacy, which posits that the data connected with a single individual (or with a statistically unrepresentative, accidental sample of individuals, which is functionally the same thing) can be used to make generalized statements about a population.

What aggregate data tell us is that we do have free will, but that this free will only operates within the constraints imposed by social structure. If I can successfully predict that most people will select X or Y but not Z, that is determinism, and the choice of Z by any single individual does not negate it.

You may also visit the True Random Number Service. Then, if you are really a glutton for punishment, check out this site.