This chapter covers several topics on probability. Because probability is the foundation of statistical methods, this chapter provides the backbone for the rest of the book. Although important, this chapter is relatively short and to the point. My intention here is not to describe at length the laws of probability but to review how probability is related to scientific endeavor in general and to statistics in particular. R.A. Fisher (1959) eloquently explains the marriage between probability and scientific inquiry: mathematical reasoning is part of inductive reasoning in science. That is, with probability we can make statements about the likelihood of the occurrence of events. According to Fisher (1959: 110), scientific inferences involving uncertainty are accompanied by ‘the rigorous specification of the nature and extent of the uncertainty by which they are qualified…’. In other words, in science we qualify statements about the occurrence of events with probability.

We will discuss the probability associated with discrete (qualitative and numerical discontinuous variables) and continuous data, and with sample means. However, before these topics are covered, we need to discuss the topic of sampling. Accordingly, this chapter is divided into five major sections:

1. random sampling and probability distributions,

2. the distribution of qualitative and discontinuous numerical variables,

3. the binomial distribution as used in biological anthropology,

4. the probability associated with continuous variables (including z scores and percentile ranks),

5. the probability distribution of sample means.