  Monte Carlo simulations are based on the manipulation of random numbers to
evaluate probable outcomes, with applicability in a variety of different
fields. By assigning probabilities, which can be determined a priori, to
various events, it is possible to track the evolution of the system over length
and time scales which are not normally accessible to other simulation
techniques. Monte Carlo simulations can provide insights, which can be used to
develop more realistic models. In this work, these simulations are used to
model a variety of probability problems normally encountered at the high school
and undergraduate level. The simulations are used to introduce concepts related
to system size, simulation runs (repeatability), and basic statistics. While
many of the problems discussed here have analytical expressions, systems where
easy analytical solutions are not available are also discussed. In this work,
MATLAB is used to model these systems and the rand function in the software is
used extensively for random number generation.
