Monte Carlo simulations of some problems; to estimate probabilities

monte_carlo.py

from random import choices, sample
from statistics import mean

def common_birthday(k):
    '''Generate k independent uniformly random birthdays & check if there are any repeats'''
    birthdays = choices(range(1, 366), k=k)
    return len(set(birthdays)) != k

>>> mean(common_birthday(23) for _ in range(10000))
0.4979

def matching(k=52):
    '''Simulates an experiment to permute 'k' cards and check if any jth card's label is j'''
    idx_labels = enumerate(sample(range(k), k))
    return any(idx == label for idx, label in idx_labels)

>>> mean(matching() for _ in range(10000))
0.6421