/* 

  The Red and the Black in Picat.

  From Martin Gardner (via Julian Simon):
  """
  Problem 1.5: The Red and the Black (from Gardner, 1983, p. 42))
  "Shuffle a packet of four cards - two red, two black - 
   and deal them face down in a row.  Two cards are picked 
   at random, say by placing a penny on each.  What is the 
   probability that those two cards are the same color?"
  """

  Cf my Gamble model gamble_the_red_and_the_black.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 : pick2
  Probabilities:
  [black,red]: 0.3352000000000000
  [red,black]: 0.3307000000000000
  [red,red]: 0.1703000000000000
  [black,black]: 0.1638000000000000
  mean = [[black,red] = 0.3352,[red,black] = 0.3307,[red,red] = 0.1703,[black,black] = 0.1638]

  var : p
  Probabilities:
  false: 0.6659000000000000
  true: 0.3341000000000000
  mean = [false = 0.6659,true = 0.3341]

*/
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() =>
  Cards = [red,red,black,black],
  Pick2 = draw_without_replacement(2,Cards),
  P     = check( Pick2.first == Pick2.second),
  
  add("pick2",Pick2),
  add("p",P).