Iıı this paper, we shall irıtroduce an important mathematical concept which has maııy applications to the probabilistic models we are considering. Iıı order to present a rigorous development of this topic, the mathematics of a considerably higher level than we are assuming here would be required. However, if we are willing to avoid certain mathematical difficulties that arise and if we are willing to accept that certain operations are valid, then we can obtain a sufficient understanding of the main ideas involved in order to use them intelligeııtly. In this paper, we made a brief summary of moment generating functions, and also we considered an application of this theory to a probability problem whose solution is impossible by hand calcu.lations.We made also a comparisoıı of biııomial distribution and Poisson distribution with the aid of moment generating functions.