# Python code for computing p-values against binomially
# distributed random variables, optimized for obviousness
# of conformance to textbook definitions.

def factorial(n):
     """ Factorial function of non-negative integers.
     """
     fact = 1
     for i in range(1, n + 1):
         fact = fact * i
     return fact

def choose(n, m):
     """ Return 'n-choose-m'.
     """
     return factorial(n) / (factorial(m) * factorial(n - m))

def binomial(n, m, p):
     """ Return the probability of exactly m hits in n independent
         trials, where each trial hits with probability p.
     """
     return float(choose(n, m)) * p**m * (1 - p)**(n - m)

def binomial_p(n, m, p):
     """ Return the probability of m or more hits in n independent
         trials, where each trial hits with probability p.
     """
     sum = 0
     for i in range(m, n + 1):
         sum += binomial(n, i, p)
     return sum