Boys.hs

{- |
Consider a family of two children. Given that there is a boy in the family,
what is the probability that there are two boys in the family?
-}

module Boys where

import Probability
 (Dist, Probability, Trans, Event,
 uniform, just, mapD, sequ, (??), (|||))


data Child = Boy | Girl
 deriving (Eq,Ord,Show)

type Family = [Child]

birth :: Trans Family
birth f = uniform [Boy:f,Girl:f]

family :: Dist Family
family = sequ [birth,birth] []

-- NOTE: could be fixed to 2
-- could be renamed to allBoys
--
boys :: Int -> Event Family
boys n = just (replicate n Boy)

existsBoy :: Event Family
existsBoy = elem Boy

-- NOTE: might not be needed, i.e., definition can be inlined instead
--
familyWithBoy :: Dist Family
familyWithBoy = family ||| existsBoy

twoBoys :: Probability
twoBoys = (boys 2) ?? familyWithBoy


countBoys :: Family -> Int
countBoys = length . filter (==Boy)

numBoys :: Dist Int
numBoys = mapD countBoys familyWithBoy