A new transform Sumudu Adomian Decomposition method (STADM) for non-linear random ordinary differential equations and the non-linear Random Integro differential equation (NRIDE) are utilized in a novel way to obtain accurate solutions. The iterative implementation of the coupled transform decomposition be use to approximated solution to ordinary differentials equation with random components. We use a normal distribution to analyze the parameters and initial conditions of ordinary differential equations with random components. Using Mathematica 13.3, the graphs of the approximate solutions and the absolute error are presented.  An investigation is conducted into the effects of the normal distribution on the results of random component differential equations. Based on the numerical results, this method is highly effective. Some applications are presented as examples of how the proposed technique can be utilized to obtain analytical or numerical solutions to certain kinds of random differential equations, thereby demonstrating its efficacy and potential.