/* 

  Urns and balls in Picat.

  Assignment 1:
  https://edu.swi-prolog.org/mod/assign/view.php?id=242
  """
  http://cplint.eu/p/urns_and_balls.swinb

  Urns and balls

  Suppose you have two urns: urn1 contains 40 blue balls and 20 red balls and urn2 contains 25 
  blue balls and 30 red balls.

  You throw an unbiased coin and, if it turns out head, you draw a ball from the first urn, 
  it it turns out tails you draw a ball from the second urn.

  Write a program modeling this process and a query for answering the question 
  "What is the probability of drawing a blue ball?"
  """

  The exact answer of drawing a blue call is 0.5*40/60 + 0.5*25/55 = 0.56060606060606060606


  Cf my Gamble model gamble_urns_and_balls.rkt

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import ppl_distributions, ppl_utils.
import util.
% import ordset.

main => go.

/*
  var : draw
  Probabilities:
  blue: 0.5597000000000000
  red: 0.4403000000000000
  mean = [blue = 0.5597,red = 0.4403]

  var : coin == tail
  Probabilities:
  tail == tail: 0.5092000000000000
  head == tail: 0.4908000000000000
  mean = [tail == tail = 0.5092,head == tail = 0.4908]

  var : coin == head
  Probabilities:
  tail == head: 0.5092000000000000
  head == head: 0.4908000000000000
  mean = [tail == head = 0.5092,head == head = 0.4908]

  var : draw == red
  Probabilities:
  blue == red: 0.5597000000000000
  red == red: 0.4403000000000000
  mean = [blue == red = 0.5597,red == red = 0.4403]

  var : draw == blue
  Probabilities:
  blue == blue: 0.5597000000000000
  red == blue: 0.4403000000000000
  mean = [blue == blue = 0.5597,red == blue = 0.4403]



*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean % ,
                           % show_percentiles,show_histogram,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  Coin = categorical([1/2,1/2],[tail,head]),
  Colors = [blue,red],

  Draw = cond(Coin == head,
              categorical([40,20],Colors),
              categorical([25,30],Colors)),

  add("draw",Draw),
  add("coin == tail",(Coin == tail)),
  add("coin == head",(Coin == head)),
  add("draw == red",(Draw == red)),
  add("draw == blue",(Draw == blue)).