ABSTRACT
This chapter presents several methods for counting outcomes in a sample space. It shows that the multiplication rule leads naturally to counting rules for sampling with replacement and sampling without replacement, two scenarios that often arise in probability and statistics. Mathematics is the logic of certainty; probability is the logic of uncertainty. Probability is extremely useful in a wide variety of fields, since it provides tools for understanding and explaining variation, separating signal from noise, and modeling complex phenomena. A good strategy when trying to find the probability of an event is to start by thinking about whether it will be easier to find the probability of the event or the probability of its complement. A story proof often avoids messy calculations and goes further than an algebraic proof toward explaining why the result is true. The chapter also presents an overview of the key concepts discussed in this book.
