In this example, we simulate flipping a fair coin (p=0.5) 10,000 times (num_trials). We use numpy to generate a binomial distribution with n=1 and p=0.5 to simulate each coin flip. We then calculate the running average of the results and plot it against the number of trials. Finally, we plot a horizontal line at the true probability of success (p=0.5) for comparison.
Note that Monte Carlo simulations can be used to simulate a wide range of probability distributions and processes, not just coin flips. The basic idea is to generate a large number of random samples from the distribution of interest and use these samples to estimate probabilities, expected values, and other properties of the distribution.
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