Probability

Abstract

The process of studying random samples from the target population and generalizing our findings to the whole population always involves dealing uncertainty. In statistical analysis of data, probability is the mathematical tool we use to quantify the extent of our uncertainty. In this chapter, we discuss some general rules of probability. We start by defining random events and then talk about assigning a probability to each event to reflect our uncertainty regarding the occurrence of that event. We discuss the union, intersection, and complement of events. We define joint, marginal, and conditional probabilities. We then use these concepts to define disjoint events and independent events. Finally, we talk about the application of tree diagrams to obtain probabilities of complex events and to make decisions under uncertainty.