Lesson 2

In code, a random experiment can be represented by a function returning an outcome, and an event by a function returning either \(\texttt{True}\) or \(\texttt{False}\). Then the Monte Carlo estimator is almost embarrassingly simple.

import random


def probability(experiment, event, trials):
    hits = 0
    for _ in range(trials):
        if event(experiment()):
            hits += 1
    return hits / trials


def flip_30_coins():
    return random.choices(["H", "T"], k=30)


def at_least_20_heads(outcome):
    return outcome.count("H") >= 20


random.seed(1)
print(probability(flip_30_coins, at_least_20_heads, 100_000))

0.04985

This program does not prove the exact value of the probability, but it gives a useful estimate. In practice, this is often enough to test intuition, to check a formula, or to choose between two engineering decisions before doing a more careful analysis.