The probability of success is difficult to estimate; but if we never search, the chance of success is zero. Probability is an independent discipline of applied Mathematics, as it requires very basic Mathematics and it is developed for resolving numerous real-life problems from ancient times, as well as designing more pragmatic game strategies for winning the game. This chapter deals with the concepts of probability, discrete probability distributions and related results through the “BEIMI” perspective. Innovative and more pragmatic examples of real life define the concepts of discrete probability distributions. The probability of getting tails in consecutive 13 times in a cricket game motivates to define the concept of Poisson distribution. Additionally, innovative applications help readers to excel understanding of the concepts in meaningful ways. The chapter concludes with case studies and exercises aimed at connecting theoretical relational structures to real world applications across various disciplines.