Regula Falsi Method, is an iterative numerical technique used to approximate solutions to nonlinear equations (algebraic or transcendental) by progressively narrowing down the intervals where the root of the equation is likely to be found. The primary goal of this work is to investigate how the probability distribution’s parameter(s) that influence a cubic polynomial’s coefficients can affect the Regula Falsi method’s convergence. This chapter examines both continuous and discrete distributions, specifically on continuous uniform distributions, discrete uniform distributions, and normal distributions. Key findings indicate that for a given parameter r, which represents the [−r, r] interval, the average number of iterations can be predicted by a second-degree polynomial equation for the uniform distributions. The coefficients of this polynomial are almost the same for both continuous and discrete uniform distributions, showing that the average iteration count depends on the distribution range rather than its type. For normal distributions, the average iteration count is influenced by the mean for fixed standard deviation, indicating the mean's critical role. In contrast, varying the standard deviation while fixing the mean shows no significant impact on the average iterations. Overall, the study concludes that for uniform distributions, the iteration count depends on the range of the distribution, while for normal distribution, it depends on the mean. Finally, a new avenue for future research is suggested, where we propose combining the Regula Falsi method with other techniques to enhance the rate of convergence and application of Regula Fasi method for system optimization is also discussed.