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This article brings up an introduction to computational physics and scientific programming through an application, the radioactive decay problem. This problem is solved computationally through two different approaches: numerical integration and stochastic simulation. The numerical integration is realised via the Runge-Kutta method, used to obtain numerical solutions of the ordinary differential equation describing the model dynamics, while the stochastic simulations are implemented via Monte Carlo simulations, where random numbers are used to guide decision making. A comparicion of the advantages of each method and its convenience is made and some examples of implementation of the algorithms presented in this work are also exhibited in different programming languages. [ABSTRACT FROM AUTHOR]