[arsenide]

If there is an analytic model, using Monte Carlo methods is extremely useful to validate the theoretical result. If both agree, it is unlikely that there is a mistake in the theoretical result: which is valuable information.

For something as straightforward as Bernoulli, where you plug values into a formula and are done, there is no reason to use MCM. However, I am in agreement that in more complicated cases (e.g. a probability distribution is based on some result of one Markov or Markov-like calculation — or possibly multiple), and the theory is slightly or much more complicated then there is a lot of value in Monte Carlo methods.