Monty Hall Problem using PFP

montyhall.scala

import scalaz.syntax.monad._
import spire.math._
import spire.implicits._

import pfp.Distribution._

// data Outcome = Win | Lose
sealed trait Outcome
case object Win extends Outcome
case object Lose extends Outcome

// firstChoice :: Dist Outcome
// firstChoice = uniform [Win,Lose,Lose]
def firstChoice = uniform[Outcome, Rational].apply(Win :: Lose :: Lose :: Nil)

// switch :: Trans Outcome
// switch Win  = certainly Lose
// switch Lose = certainly Win
def switch(o: Outcome) = o match {
  case Win => certainly[Outcome, Rational](Lose)
  case Lose => certainly[Outcome, Rational](Win)
}

firstChoice.plot
//
//  Win 1/3 #################################
// Lose 2/3 ##################################################################
//

(firstChoice >>= switch).plot
//
//  Win 2/3 ##################################################################
// Lose 1/3 #################################
//