Fun with Probability

gistfile1.rb

# to run this file:
# gem install rspec
# rspec prob_spec.rb

class Integer
  def factorial
    self.downto(1).inject(:*)
  end
end


class Dice
  attr_accessor :number_of_choices, :choice_labels, :probabilities, :sides
    
  def initialize number_of_choices, choice_labels, probabilities
    @number_of_choices  = number_of_choices
    @choice_labels      = choice_labels
    @probabilities      = probabilities
    @sides              = Hash.new 

    raise "probability values do not add up to 1" unless probabilities.inject(:+) == 1
    
    choice_labels = [ choice_labels ] if choice_labels.class == String # convert to array if we're being passed a single side
    choice_labels.each_with_index{ |choice, n| @sides.merge!( choice => probabilities[n] ) }
  end

  def method_missing(*args)
    # args[0] is the method name called
    if args.length == 2 and args[0] == :call and args[1].class == String
      @sides[ args[1] ]
    else
      super
    end
  end
end


class Solve
  attr_reader :dice
  protected :dice

  def initialize d
    @dice = d
  end  
  
  def prob_of_ordered_events events
    events.inject(1){|product, e| product * @dice.sides[e] }.round(4) 
  end

  def prob_of_unordered_events events
    self.choose(events.size, events.count(events.last), nil) * prob_of_ordered_events(events)
  end

  def choose n, k, d
    n.factorial / ( k.factorial * (n-k).factorial)
  end
end


describe "Dice" do
  context "in context to initializing class variables" do
    it "should allow you to configure the number of sides for a dice, with each side having a label, and a unique probability" do
      dice = Dice.new(2, ["heads","tails"], [0.5,0.5])
      dice.number_of_choices.should == 2
      dice.choice_labels.should == ["heads","tails"]
      dice.("heads").should == 0.5
      dice.("tails").should == 0.5
    end

    it "should fail if you give it probability values that do not add up to 1" do
      expect { Dice.new(1,["heads"],[0.9]) }.should raise_error
    end

    it "should support dice with 1 side" do
      dice = Dice.new(1,["heads"],[1.0])
      dice.number_of_choices.should == 1
    end
  end
end


describe "Solve" do
	it "should solve for the probability of a list of ordered events" do
		four_sided_die = Dice.new(4, ["1","2","3","4"], [0.20,0.20,0.20,0.40])
		Solve.new(four_sided_die).prob_of_ordered_events(["1","4","2"]).should == 0.016
	end
	
	it "should solve for the probability of a set of unordered events" do
		two_sided_die = Dice.new(2,["heads","tails"],[0.5,0.5])
		Solve.new(two_sided_die).prob_of_unordered_events(["tails","heads"]).should == 0.5
		Solve.new(two_sided_die).prob_of_unordered_events(["heads","tails"]).should == 0.5
	end
	
	it "should solve for the probability of a choice of events" do
		one_sided_die = Dice.new(1,"only side",[1.0])
		#Given 3 Dice and 5 Buckets, how many ways are there to place the Dice in the Buckets
		#Also known as k Choose n or 5 choose 3
		Solve.new(one_sided_die).choose(5, 3, one_sided_die).should == 10
	end
end