This chapter is concerned with special probability distributions and techniques used in calculations of reliability and risk. It treats the general subject of probability, particularly as it applies to hazards and events. The chapter introduces several probability distribution models that are extensively used in reliability calculations in hazard risk assessment. The primary causes of accidents in the industry are mechanical failure, operational error, process upsets, and design errors. The majority of industrial facilities and process plants utilize many series of parallel configurations. One way to express the likelihood quantitatively is to use a numerical value, termed the probability, to express its likelihood of occurring. The chapter provides general properties of various probability distribution function for discrete and continuous random variables, as well as an introduction to the cumulative distribution function. It concludes with a consideration of fault tree analysis, a special technique that figures prominently in hazard analysis and the evaluation of risk.