/* 

  Three children paradox in Picat.

  From https://ali.medium.com/3-probability-paradoxes-challenging-our-understanding-of-chance-01d950affc9b
  """  
  Let’s consider a family with three children and analyze the probability that all 
  these children will be of the same gender. Intuitively, one might think that since 
  the first two children are bound to be of the same gender, the odds of the third child 
  being the same gender should be 1/2.

  However, a closer examination of the probability reveals a different story. If we represent 
  girls by ‘G’ and boys by ‘B,’ there are eight possible combinations: BBB, BBG, BGB, GBB, 
  BGG, GBG, GGB, and GGG. Out of these combinations, only BBB and GGG consist of all 
  boys or all girls, respectively, meaning the actual probability of all three children 
  being the same gender is 2/8 or 1/4, not 1/2, as initially assumed.
  """

  Cf my Gamble model gamble_three_children.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 : children
  Probabilities:
  [girl,boy,boy]: 0.1279000000000000
  [boy,boy,girl]: 0.1265000000000000
  [boy,boy,boy]: 0.1259000000000000
  [boy,girl,girl]: 0.1255000000000000
  [girl,girl,girl]: 0.1252000000000000
  [girl,girl,boy]: 0.1245000000000000
  [girl,boy,girl]: 0.1226000000000000
  [boy,girl,boy]: 0.1219000000000000

  var : p
  Probabilities:
  false: 0.7489000000000000
  true: 0.2511000000000000
  mean = 0.2511

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean % ,
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  N = 3,
  Children = categorical_n([1/2,1/2],[boy,girl],N),

  P = check( Children.remove_dups.len == 1),
  
  add("children",Children),
  add("p",P).