Brownian motion plays a very important role in both stochastic process and Schramm Loewner Evolution (SLE). Firstly

by using the properties of Brownian motions

it is derived that the probability expressions of Brownian motion exiting first at prescribed boundary parts of regions. The correctness of the obtained results is verified by numerical simulations. Secondly

the relationship between harmonic measure and probability of Brownian motion exiting first a simply connected domain at the specified boundary is discussed. The probability formulas of the former are derived by using the results of the latter. In addition

some other related results are obtained.