The tuesday birthday problem

tuesday_birthday.py

import random

print '''
You meet a man on the street and he says, "I have two children and one is a son born on a Tuesday."
What is the probability that the other child is also a son?
'''

def get_combinations():
  children = ('s', 'd')
  weekdays = tuple(range(1, 8))
  known_kid = ('s', 2)

  def valid_combination(x, y, z, w):
    return (x, z) == known_kid or (y, w) == known_kid

  return [(x, y) for x in children for y in children for z in weekdays for w in weekdays if valid_combination(x, y, z, w)]

def test(num_tests):
  "Benchmark to convince people that the answer is not 1/2"
  combinations = get_combinations()

  def increase_if_two_sons(accumulator, _):
    if random.choice(combinations) == ('s', 's'): accumulator += 1
    return accumulator

  num_two_sons = reduce(increase_if_two_sons, [None] * num_tests, 0)

  print "Probability: %.2f" % ((float(num_two_sons) / num_tests) * 100)
  print "Estimated Probability: %.2f" % (13.0 / 27 * 100)

test(1000000)