#!/usr/local/bin/python3

# Classic birthday problem. What is the probability that in a room with n people, at least two people will have the same birthday.
# Input n -- number of people in room
# Return  -- probability that at least two people will share a birthday

def any_birthday_match(n):
    if n > 365:
        result = 1
    elif n < 2:
        result = 0
    else:
        prob = 1.0
        for i in range(364, 365 - n, -1):
            prob *= i / 365
        result = 1 - prob
        
    return result

# Probability that in a room of n OTHER people at least one person will share your birthday.
# Input n -- number of people in room
# Return  -- probability that at least one other person will share your birthday

def specific_birthday_match(n):
    if n < 1:
        result = 0
    else:
        result = 1 - (364 / 365) ** n

    return result
        
if __name__ == "__main__":
    import sys
    n = 23
    result = any_birthday_match(n)
    s = 'In a group of {0:d} people, the probability of two people sharing the same birthday is {1:.4f} .'.format(n, result)
    print(s)
    n = 253
    result = specific_birthday_match(n)
    s = '\nIn a group of {0:d} other people, the probability of someone having your birthday is {1:.4f} .'.format(n, result)
    print(s)
    
# End of code:
    
# In a group of 23 people, the probability of two people sharing the same birthday is 0.5073 .

# In a group of 253 other people, the probability of someone having your birthday is 0.5005 .