The modern trend in the development of error correcting codes is to use the techniques of stochastic analysis. This outlook has lately produced the Tornado codes, Fountain codes, Luby transform (LT), and Raptor codes, as described in the following chapters. The background material for such a direction in the evolution of ECC is presented in this chapter. As James Grover Thurber (1894-1961) has so aptly said, “A pinch of probability is worth a pound of perhaps.” Out of all possible distributions only the ones with direct application to the above-mentioned codes are presented.