Probability and statistics are deductive and inductive tools, respectively, that are used to deal with uncertainty. Probability concepts and values are used in both deductive and inductive reasoning, and inductive problems often contain deductive subproblems, so probability theory is needed to handle diverse contexts. Probability is important because in many cases the best answers that science can deliver are more or less probable conclusions, rather than absolute certainties. Daily life and scientific research are full of unavoidable practical decisions that must be made on the basis of the best available information.

Correct probability reasoning is not easy. Indeed, probability blunders are among the most common kinds of blunders, even in professional, refereed scientific journals. Regulatory agencies and law courts can perpetuate such blunders, as they often rely on scientific findings, thereby inflicting wrongful losses and injustices. The challenge in probability reasoning is that it requires some precise distinctions that are critical for getting the correct results, but those distinctions are not intuitively obvious, and few scientists learn or teach them. Also, there are conflicting paradigms that can seriously affect research efficiency and technological progress, but precious few scientists understand the issues. So there is much to be gained from a proper understanding of probability and statistics, as pursued in this and the next chapters.

This chapter cannot possibly do what an entire book on probability would do: present a comprehensive treatment.