Can probabilities be added?
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In general, one cannot add probabilities.
What is a Monte Carlo simulation?
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A simulation which arrives at an approximation of a probability by running many, many trials.
What is the guiding principle of inferential statistics?
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A random sample tends to exhibit the same properties as the population from which it is drawn.
What is the law of large numbers (a.k.a. Bernoulli's Law)?
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The law of large numbers basically says that using more test cases in a simulation involving randomness will increase our confidence in its results.
What is the gambler's fallacy?
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The belief that random numbers will even out constantly (e.g. that after a string of heads, it's “time for” the coin to come up tails.)