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Monte Carlo algorithms use randomness to produce a result where correctness has a probability less than 1 but can be approximated with repeated trials. An example application is estimating the value of $\\(pi\\)$ by random sampling of points within a square and counting how many fall inside a quarter-circle.

Randomized primality tests, such as the Miller-Rabin test, use randomness to determine if a number is prime. It offers a probable prime assessment with a small chance of error, which decreases exponentially with more iterations of the algorithm.

Las Vegas algorithms use randomness to always produce a correct result, but the amount of time taken to produce the result is not fixed. An example of this is the QuickSort algorithm, which uses randomness in choosing the pivot element to ensure good average performance.

Randomized load balancing algorithms distribute tasks among multiple servers or processes. Random choices are used to assign tasks, which statistically leads to a fair distribution of load. An example is the 'Power of Two Random Choices', which picks two servers at random and assigns the task to the less loaded one.