Fraction of the population that are girls if every couple keeps having children until they have a boy

girlFraction

# http://www.thebigquestions.com/2010/12/21/are-you-smarter-than-google/

# There’s a certain country where everybody wants to have a son. 
# Therefore each couple keeps having children until they have a boy; 
# then they stop. What fraction of the population is female? (30.7%)

# Probability   Configuration
#    1/2              B
#    1/4              GB
#    1/8              GGB
#    1/16             GGGB

# Expected number of boys is 
# (1/2)*1 + (1/4)*1 + (1/8)*1 + ... = 1

# Expected number of girls is 
# (1/2)*0 + (1/4)*1 + (1/8)*2 + ... = 1

# Expected fraction of girls is
# (1/2)*0 + (1/4)*(1/2) + (1/8)*(2/3) + ... = 1-log(2)

topfrac=1.0
botfrac=2.0
probability = 1.0/2.0
i=0
sum=0

while (i < 100)
  probability/=2
  sum+=(topfrac/botfrac)*probability
  topfrac+=1
  botfrac+=1
  i+=1
end

solution = 100-(Integer((1-sum)*1000)/10.0)

puts "The percentage of girls is approximately #{solution}%"