# The tuesday boy problem
# http://s...content-available-to-author-only...s.com/evolutionblog/2011/11/08/the-tuesday-birthday-problem/
# http://e...content-available-to-author-only...a.org/wiki/Boy_or_Girl_paradox
# Sounds complicated and counter-intuitive, right?
# Python to the rescue!
 
# I have changed the wording in the problem to be less ambiguous:
# "If you ask someone whom you know has two children, whether they have
#  at least one boy born on a tuesday, what is the probability that
#  both children are boys?"
 
import itertools
import fractions
 
GENDERS = 'boy girl'.split()
DAYS = 'mon tue wed thu fri sat sun'.split()
 
def has_two_boys((child1, child2)):
    #Do you have two boys?
    return child1[0] == 'boy' and child2[0] == 'boy'
 
def question(child):
    #Is this child a boy born on a tuesday?
    return child == ('boy', 'tue')
 
def show_probability(pairs):
    nr_boy_pairs = len(filter(has_two_boys, pairs))
    print '%d pairs, where %d are boy pairs' % (len(pairs), nr_boy_pairs)
    print 'gives', fractions.Fraction(nr_boy_pairs, len(pairs))
    print
 
CHILD_TYPES = list(itertools.product(GENDERS, DAYS))
#All these pairs are equally common
#(if we pretend that each day and gender is equally likely for each birth):
ALL_CHILD_PAIRS = list(itertools.product(CHILD_TYPES, CHILD_TYPES))
 
print 'Probability that a person has two boys:'
show_probability(ALL_CHILD_PAIRS)
 
#Now we ask all parents the question
YES_PARENTS = [pair for pair in ALL_CHILD_PAIRS
               #Is any of your children a boy born on a tuesday?
               if question(pair[0]) or question(pair[1])]
 
print 'Probability that a person has two boys, given that they answer yes:'
show_probability(YES_PARENTS)
 

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