Monte Carlo Algorithms
Monte Carlo algorithms are always fast, and probably correct. There are two kinds of Monte Carlo algorithms: one-sided and two-sided.
One-sided algorithms can disprove something, but never prove it beyond a shadow of a doubt. Multiple runs can give the verity of the tested assertion some confidence, but there is always a chance that it may still be incorrect. Examples of one-sided Monte Carlo algorithms include random sampling, abundance of witnesses, and interactive proofs.
Two-sided algorithms (also known as Atlantic City algorithms) always provide a yes/no answer, but there is a chance that the answer might be incorrect. Fingerprinting is a good example of a two-sided Monte Carlo algorithm.