This thesis investigates switching transients in a test system comprised of a single-core underground cable, vacuum circuit breaker, and (Y-Y) star transformer. This work presents six scenarios in which test systems are connected to the transformer in different load scenarios such as no-load, medium and high loads, low and high capacitance, and a combined impedance-capacitance case. Monte Carlo simulations have been employed to introduce random variability into the parameters of vacuum circuit breaker(VCB) to enable probabilistic analysis of extreme transients. Using EMTP and MATLAB software, the study confirms how probabilistic transient analysis can be utilized to improve power system reliability and design protective switchgear.