This chapter introduces four important distributions that can be used to describe a variety of situations. The first distribution encountered is that of the binomial distribution (Section 5.2). This is used to understand problems where the possible outcomes are binary, and usually categorised in terms of success and failure. For example, one can consider the situation of either detecting of failing to detect a particle passing through some apparatus as a binary event. The detection efficiency in this particular problem is the parameter p of the binomial distribution. Typically one finds that p ~ 1 when working with efficient detectors. The Poisson distribution (Section 5.3) can be used to understand rare events where the total number of trials is not necessarily known, and the distribution depends on only the number of observed events and a single parameter λ that is both the mean and variance of the distribution. For example, the Poisson distribution can be used to describe the uncertainties on the content of each bin in Figure 1.2, which is a topic discussed in more detail in Chapter 7. The third distribution discussed here is the Gaussian distribution (Section 5.4). This plays a significant role in describing the uncertainties on measurements where the number of data are large. Finally the X2 distribution is introduced in Section 5.5.