BiasedCoin.py

# I have a biased coin that lands heads up with
# probability p and tails up with probability (1-p). I
# toss the coin n times. What is the probability that I
# will see at least k heads?
#
# https://www.quora.com/I-have-a-biased-coin-that-lands-heads-up-with-probability-p-and-tails-up-with-probability-1-p-I-toss-the-coin-n-times-What-is-the-probability-that-I-will-see-at-least-k-heads

def product(xs):
  p = 1
  for i in xs:
    p *= i
  return p

def factorial(n):
  return product(range(1, n+1))

def choose(n, i):
  return factorial(n)/(factorial(i)*factorial(n-i))

def atleast_k_heads(n, k):
  return sum(choose(n,i) * p**i * (1-p)**(n-i) for i in range(k, n+1))