Randomized methods are techniques that incorporate randomness into their processes to solve problems or make decisions. These methods are often used in fields like statistics, computer science, and machine learning to improve efficiency and accuracy. By introducing randomness, these methods can explore a wider range of possibilities and avoid getting stuck in local optima. One common application of randomized methods is in Monte Carlo simulations, where random sampling is used to estimate complex mathematical functions or physical systems. Another example is randomized algorithms, which use random inputs to achieve faster solutions for problems like sorting or searching, often with a guarantee of performance over time.