/* 

  Rolling two dice which sums to 8 in Picat.

  From 
  https://medium.com/math-games/can-you-do-this-not-so-hard-probability-puzzle-40a502dfbc15
  """ 
  Suppose two fair dice are rolled and their sum is 8.
  What's the probability that at least one die lands on 4?
  """

  The probability is 1/5 (0.2)

  Cf my Gamble model gamble_two_dice_sum.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 : p
  Probabilities:
  false: 0.7986650221287093
  true: 0.2013349778712907
  mean = 0.201335

  var : d1
  Probabilities:
  4: 0.2013349778712907
  3: 0.2008271058550388
  2: 0.2006094464195023
  5: 0.1992309366611043
  6: 0.1979975331930639
  mean = 3.99318

  var : d2
  Probabilities:
  4: 0.2013349778712907
  5: 0.2008271058550388
  6: 0.2006094464195023
  3: 0.1992309366611043
  2: 0.1979975331930639
  mean = 4.00682

*/
go ?=>
  reset_store,
  run_model(100_000,$model,[show_probs_trunc,mean
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  D1 = dice(),
  D2 = dice(),  

  S = D1 + D2,

  observe(S == 8),

  P = check( (D1 == 4, D2 == 4) ),

  if observed_ok then
    add("p",P),
    add("d1",D1),
    add("d2",D2),
  end.