Monte Carlo simulation of "Boy or Girl" paradox

boygirl.py

#!/usr/bin/env python3

"""
I go around, knocking on people's doors, until I find someone with two
children, at least one of which is a boy.

What is the probability that they are both boys?

(The answer should approximate 1/3.)

"""

from itertools import islice
from random import choice


N = 1000000

SEXES = 'Boy Girl'.split()


def main(n_tries):

    def pick_pair():
        return (choice(SEXES), choice(SEXES))

    def condition(children):
        return any(child == 'Boy' for child in children)

    def event(children):
        return all(child == 'Boy' for child in children)

    print(monte_carlo(pick_pair, condition, event, n_tries))


def monte_carlo(sample, condition, event, n_tries):
    space = filter(condition, infinitely(sample))
    n_success = 0
    for case in islice(space, n_tries):
        if event(case):
            n_success += 1
    return n_success / n_tries


def infinitely(f):
    while True:
        yield f()


if __name__ == '__main__':
    main(N)

boygirl2.py

#!/usr/bin/env python3

"""
I go around, knocking on people's doors, until I find someone with two
children, at least one of which is a boy *who is born on Tuesday*.

What is the probability that they are both boys?

(The answer should approximate 13/27.)

"""

from collections import namedtuple
from itertools import islice
from random import choice


N = 1000000

SEXES = 'Boy Girl'.split()
DAYS = 'Sun Mon Tue Wed Thu Fri Sat'.split()

Person = namedtuple('Person', 'sex day')


def main(n_tries):

    def pick_child():
        return Person(choice(SEXES), choice(DAYS))

    def pick_pair():
        return (pick_child(), pick_child())

    test = Person('Boy', 'Tue')
    def condition(children):
        return any(child == test for child in children)

    def event(children):
        return all(child.sex == 'Boy' for child in children)

    print(monte_carlo(pick_pair, condition, event, n_tries))


def monte_carlo(sample, condition, event, n_tries):
    space = filter(condition, infinitely(sample))
    n_success = 0
    for case in islice(space, n_tries):
        if event(case):
            n_success += 1
    return n_success / n_tries


def infinitely(f):
    while True:
        yield f()


if __name__ == '__main__':
    main(N)