Probability

This chapter introduces the concepts, tools, and techniques of probability in an intuitive way. The study of probability became an essential part of statistics owing to the obvious reason that probability is deep rooted in a great majority of statistical models and procedures. Popular ways to express a probability are fractional form, decimal form, scientific form, percentage form, literal form, pictorial form, and as tail areas under empirical curves or functions. The chapter focuses mostly on probability mechanisms involved in random experiments. Events can be combined using set theoretic operations union, intersections, complements, and differences. The chapter discusses sample space, permutations and combinations, and also about the principle of inclusion and exclusion (PIE). This is followed by a discussion on recurrence relations, urn models and partitions. Finally, the chapter talks about conditional probability, including Bayes theorem.