This article studies the dependence of the daily total solar radiation during a given day on the daily total solar radiation of the previous day, for a location in southwestern Greece. Fourteen years dataset of daily total solar radiation is used. This data is classified in two subsets, namely, one of "good" and a second of "bad" weather. The conditional probabilities of the daily clearness index "good-to-good" weather, P 1 1, and "bad-to-good" weather, P 0 1, are calculated. A satisfactory fitting of the obtained probabilities to parametric mathematical equations, is proposed. For solar energy applications, the first-order two-state Markov model is described by a Bernoulli random variable. Therefore, a sequence of "good" or "bad" weather of k consecutive days has been estimated by applying the equations of the Bernoulli distribution. The results of this work can be used in several solar energy system calculations, such as for weather data generation in solar simulation processes.