Fundamentals of Probability

This chapter introduces probability concepts and useful notation that are most pertinent to biomedicine and biostatistical analysis, and introduces several basic operations of events using set language, and use Venn diagrams to express that relationship. The chapter discusses the dependence and independence of events using conditional probability. Probability is a measure of the likelihood of the occurrence of an event, which is an inherent property of things. It can be approximated by relative frequency through a large number of repeated experiments under the same conditions, which makes probability easy to understand and calculate intuitively. Probability can be calculated using the addition law and multiplication law when the events satisfy the corresponding conditions. The basic idea of total probability formula and Bayes' rule is to divide a composite event into several mutually exclusive events, calculate the probabilities of these events separately, and use the addition law and multiplication law of probability to obtain the final result.