In a Discrete Stochastic System described by a Markov Jump Process fluctuations can drive the state variables to regions that are forbidden in the deterministic, continuum description of the system. These rare, large deviation events with exponential waiting times will be analyzed on two benchmark systems: SIS Model from Epidemiology and Schlögl Model from Chemical Kinetics. The diffusion approximation is shown to fail to properly capture mean waiting times of rare events. I will also describe certain large deviations techniques to get the correct waiting time exponents bypassing the exact solutions. Furthermore, in multistable systems the paths that contribute most to the mean first passage times between two states are not always the most likely ones. This new, but simple result will be illustrated on a bistable model with exact solutions available at hand.