In attempting to analyze insurance losses arising in connection with health coverages as well as property and casualty insurance situations involving homeowner and automobile coverages, it is imperative to understand that a portfolio of insurance business is quite complicated in terms of the nature of its past and future risk-based behaviour. There are many deterministic and stochastic influences at play, and the precise prediction of the future claims experience necessitates that all such influences and their effects be identified. The role of probability and statistics is vitally important in this regard, not only in terms of providing the required statistical methodology to properly analyze any data collected by the business but also in assessing whether a quantitative (i.e. theoretical) model is able to accurately predict the claims experience of a portfolio of insurance business.