bday.py

#!/usr/bin/env python

"""
Given n people what's the probability that there is a
birthday on each day of the year (assuming equal prob
for each day & no leap year)?
"""

import random

rand = random.SystemRandom()

def assign_n(n):
    global rand
    DAYS = 365

    day_indexes = set(range(DAYS))
    for i in xrange(n):
        index = rand.randrange(0, DAYS)
        day_indexes.discard(index)
        if len(day_indexes) == 0:
            return True
    return False

def main():
    TRIALS_PER_N = 200
    for N in xrange(2000, 2500):
        positive_trials = 0
        for trial_index in xrange(TRIALS_PER_N):
            passed = assign_n(N)
            if passed:
                positive_trials += 1
        percentage = positive_trials / float(TRIALS_PER_N)
        print 'N: %d, prob: %f' % (N, percentage)


if __name__ == '__main__':
    main()