Just about the most satisfying piece of code I've ever written.

probably.py

#!/usr/bin/env python3
from fractions import Fraction
from itertools import product
import statistics
import random
import logging

from matplotlib import pyplot as plt, style

logging.basicConfig(level=logging.DEBUG)


def probability(event, sample_space):
    return Fraction(len(event), len(sample_space))


def trial(S):
    return random.choice(S)


def simulate(n):
    for i in range(n):
        yield trial(S)


if __name__ == '__main__':
    # sample space, i.e. all possible outcomes
    # NOTE: _Not_ a set of "intermediate results", but of the same "type" as the
    # results contained in A _and_ can be "filtered" by a boolean
    S = [sum(i) for i in product({*range(1, 7)}, range(1, 7))]
    assert len(S) == 6 * 6  # i.e. 2 six-sided die
    assert probability(S, S) == 1  # rule
    A = list(filter(lambda x : x <= 9, S))

    P = probability(A, S)
    P

    plt.hist(S)
    plt.hist([*simulate(100)])
    plt.hist([*simulate(1000)])