Birthday paradox

birthday_paradox.py

from __future__ import division
from operator import mul


def Q(n):
    """
    Let Q(n) be the probability that     
    no two people have a common birthday.

    """
    y = 365
    
    # The number of n birthdays without any duplicates.
    dd = reduce(mul, range(y - n + 1, y + 1))

    # The total number of n possible birthdays.
    dr = y ** n

    return dd / dr


def P(n):
    """Let P(n) be the probability in question."""
    return 1 - Q(n)


print P(30)
print P(23)