The Birthday Problem in Python.

birthday.py

from random import randint
from collections import defaultdict

def tally_k_birthdays( k):
    counts = defaultdict( int)
    for i in range( 0, k):
        birthday = randint( 1, 365)
        counts[ birthday] += 1
    return counts

def identify_same_birthdays( counts_of_birthdays):
    for day in counts_of_birthdays.keys():
        if counts_of_birthdays[ day] > 1:
            return True
    return False

def sample_group( size, times):
    match = 0.0
    for i in xrange( times):
        birthday_count = tally_k_birthdays( size)
        if identify_same_birthdays( birthday_count):
            match += 1.0
    return match / times
    
print sample_group( 23, 1000)