ABSTRACT
This chapter introduces the probability of events both mathematically and through Monte Carlo simulation. The student learns the concepts of statistical experiments, outcomes and events, and basic elementary set operations. Probability is defined axiomatically, followed by computational rules for finite operations on events. Some counting arguments are included, with traditional applications to dice, coin flipping and cards. The emphasis quickly turns to Monte Carlo simulation, using the law of large numbers to estimate probabilities of more complicated events. The main R tools used for simulation are sample and replicate and they are thoroughly explored. Conditional probability and independence are treated computationally, through simulation, and intuitively. Key concepts of Bayes’ Rule and the Law of Total Probability are introduced. A vignette on negative surveys is included for students with a basic knowledge of linear algebra.
