In this thesis we introduce probability theory adapted on time scales. In this study, we have modified some concepts of probability theory on time scales...Probability Function has been constructed on time scales. After providing some basic concepts of Probability Theory, the review of the fundamental concepts of time scale has been provided. Time scale unifies continuous and discrete analysis. With the help of the definition of ..Measure and the ..Probability Function, random variable has been constructed on time scale. Mathematical expectation and some probabilistic inequalities are provided to Time scale.