/* 

  Two heads in three coin tosses in Picat.

  From Statistics101 (Resample Stats)
  http://www.statistics101.net/QuickReference.pdf
  Page 9
  """
  (S)ay you wanted to know the probability of getting exactly two heads
  in a toss of three coins.
  """

  Picat> println(binomial_dist_pdf(3,1/2,2).and_rat)
  0.375 (3 / 8)


  Cf my Gamble model gamble_two_heads_in_three_coin_tosses.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 : c
  Probabilities:
  1: 0.3767000000000000
  2: 0.3681000000000000
  3: 0.1286000000000000
  0: 0.1266000000000000
  mean = 1.4987

  var : p
  Probabilities:
  false: 0.6319000000000000
  true: 0.3681000000000000
  mean = 0.3681

  theoretical = 0.375 (3 / 8)

*/
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,
   println(theoretical=binomial_dist_pdf(3,1/2,2).and_rat),
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  Coin = [head,tail],
  Tosses = resample(3,Coin),
  C = count_occurrences(head,Tosses),
  P = check(C == 2),
  
  add("c",C),
  add("p",P).