What role does random sampling play in Monte Carlo simulation?

Random sampling is a fundamental component of Monte Carlo simulation that enables the estimation of probabilities of various outcomes within a modeled system. In a Monte Carlo simulation, random samples are drawn from known probability distributions to represent possible inputs or scenarios. By repeatedly simulating the process with these varying inputs, the simulation generates a range of possible outcomes. This allows analysts to assess the likelihood of different results emerging from a stochastic model.

The essence of Monte Carlo methods lies in their ability to leverage randomness to explore a wide array of scenarios. As the number of random samples increases, the approximation of the probabilities of various outcomes improves, providing a clearer picture of risk, uncertainty, and potential paths forward.