Uncertainty is very much a part of the world in which we live. Indeed, one often hears
the well-known cliche that the only certainties in life are death and taxes. However,
even these supposed certainties are far from being completely certain, as any actuary or
accountant can attest; for although one's eventual death and the requirement that one pay
taxes may be facts of life, the timing of one's death and the amount of taxes one must
pay are far from certain and are generally beyond one's control.
Uncertainty can make life interesting. Indeed, the world would likely be a very dull
place if everything were perfectly predictable. However, uncertainty can also cause grief
and suffering. For example, the sudden and premature death of a family breadwinner
can cause great financial distress for surviving family members with limited means of
support. The age-old fascination of humans with predicting the future, as evidenced
by the ever-present popularity of astrology and fortune-telling, and the development of
institutions such as insurance to make the effects of an uncertain future less severe are
no doubt due in large part to a recognition of the malevolent role that uncertainty can
play in one's life.
This book presents the scientific approach to uncertainty, known as probability, which
has been developed over the past 350 years and is generally accepted in the scientific
community. There are undoubtedly many other approaches, such as mysticism and
astrology, which some people use to understand uncertainty. However, these approaches
lie beyond the realm of science and will not be considered in this book.
In this introductory chapter, we consider what the nature and scope of probability
is and how it arises in engineering and the sciences. We also consider how the notion
of a probability should be defined and how it can be interpreted. We then discuss how
probability models are constructed in practice. We end this introductory chapter with an
outline of the topics covered in the rest of the book.
What Is Probability?
Probability is the branch of science concerned with the study of mathematical techniques
for making quantitative inferences about uncertainty. The key words in this definition
are quantitative and inferences. Indeed, as we will soon see, probability provides a
mechanism for making quantitative statements about uncertainty and, more important,
allows one to draw quantitative conclusions from such statements using the rules of logic.