The definition of a random variable and its probability distribution is discussed, and the concept of expectation as averaging in a population is introduced. The Bernoulli trial is presented and its importance as the basis for many other distributions is emphasized. This is followed by coverage of the binomial distribution following a general format used for probability distributions throughout the book: derivation; applications; generation of random deviates; and fitting the distribution to data. The hypergeometric distribution is presented as a finite population analogue of a binomial distribution. The negative binomial distribution is related to a sequence of Bernoulli trials. The Poisson distribution is defined relative to a Poisson process and derived as a limit of a binomial distribution. Spatial Poisson processes are introduced. The chapter ends with: a summary of: notation used; the main results, MATLAB and R syntax; and exercises.