There are many probability distributions that are useful in describing common phenomena in the manufacturing and service industries.  Also called probability mass functions (PMFs), they can be used to answer questions regarding product quality, machine reliability, or process performance.  Several of the common distributions are discussed in this paper.  The term expected value of X, denoted as E(X), will be used as the average number that would be expected over a large number of trials.  Success is defined by the experimenter and could mean either pass or fail, blue or red, heads or tails, or any other metric depending on the situation.