The theory of time scales has been introduced to unify discrete and continuous analysis. In this talk, we will discuss the elements of probability theory and concept of Brownian motion on general time scales. After presenting a brief introduction on the subject, probability measure derived from Lebesgue Δ-measure, probability density function and generalized normal distribution on time scales will be given. After that, Brownian motion on time scales will be introduced and its quadratic variation will be derived.