Abstract: Human lives are full of uncertainties as with many natural phenomena. No one can precisely foresee what will happen in the next second, minute and so on. The sample realization of a stochastic process are vital from the point of view of Brownian path analysis. A Brownian Motion (BM) with drift zero and diffusion coefficient, one is defined as standard BM whose path properties are used for analysis in several physical and chemical problems. Rather than accepting the fact that the future is always uncertain, many models and algorithms have been continuously formulated for the prediction of matters involving uncertain elements. One of them is the Brownian model. In this study, we discuss the enhanced path properties of a one dimensional standard Brownian motion B(t), t≥0 on a complete probability space (Ω, F, P). The law of the iterated logarithm about how Brownian Motion (BM) oscillates in a neighbourhood of the origin is also discussed.