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I got a question from someone in my office who is taking a class on research methods. She asked me to define the term "Monte Carlo" that her teacher had used without much of an explanation.
Monte Carlo is a method that studies a problem by repeatedly simulating the random components of the problem and examining the average result. It always provides an approximate answer, but if the random components are accurately specified and if the number of repetitions is large enough, the accuracy of a Monte Carlo simulation can be quite good.
You should avoid the use of Monte Carlo methods when an exact answer is available through mathematics (except perhaps, as a learning experience).