group_of_girls.rb

=begin
On Friday afternoon, our instructor put us into groups of three for a quiz.
A girl in our class ended up in a group of all girls and asked:
"What are the odds of there being in an all girl group?"

While the girl who asked the question did not expect a serious answer, the
question piqued my curiosity. The easiest way to get the answer is by
simulation and hence this script was created.
=end


class GroupOfGirls

  # Our class had 6 girls and 6 guys
  STUDENTS = [:f,:m] * 6

  def initialize
    @number_of_trials = 1e7
    @favourable_outcomes = 0
  end

  def trial
    students = STUDENTS.shuffle
    until students.empty?
      if (students.pop 3).all_girls?
        @favourable_outcomes += 1
        break
      end
    end
  end

  def simulate
    @number_of_trials.to_i.times do
      trial
    end
  end

  def results
    result = @favourable_outcomes/@number_of_trials * 100
    puts "The probability of there being at least one all girl group is"
    puts "approximately #{ result.round(2) }%"
  end

end

class Array
  def all_girls?
    self == [:f] * 3
  end
end

g = GroupOfGirls.new
g.simulate
g.results

# => The probability of there being at least one all girl group is 
#    approximately 35.71%

The exact probability of at least one all-girl group is 5/14. The probability that the girl will be assigned to an all-girl group is 2/11.