Birthday Problem

def sameBirthdayInCrowd(n):
    if n != int(n) or n <= 0 or n > 365:
        return None
    product = 1
    for i in range(n):
        product *= (365 - i)/365
    return 1 - product

def sameBirthdayWithMe(n):
    if n != int(n) or n <= 0:
        return None
    return 1 - (364/365)**n

# MAIN FUNCTION
numbers = list(range(1, 366))
import matplotlib.pyplot as plt
plt.plot([sameBirthdayInCrowd(n) for n in numbers], label="Same Birthday in crowd of n people")
plt.plot([sameBirthdayWithMe(n) for n in numbers], label="Same Birthday with me in crowd of n people")
plt.xlabel("n")
plt.ylabel("f(n)")
plt.legend()
plt.show()