/* 

  Flipping three coins in Picat.

  From http://www.statistics101.net/statistics101web_000007.htm
  """
  From CliffsQuickReview Statistics, p. 38, example 1 
  What is the probability of simultaneously  
  flipping 3 coins and having them all land heads?  
  """

  Exact:
  Picat> pdf_all($binomial_dist(3,1/2)).sort_down(2).printf_list 
   2 0.375 
   1 0.375 
   3 0.125 
   0 0.125 

  Picat> X=binomial_dist_pdf(3,1/2,3)  
  X = 0.125

  Picat> X = pdf($binomial_dist(3,1/2),3)
  X = 0.125

  Cf my Gamble model gamble_flipping_three_coins.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 : heads
  Probabilities:
  2: 0.3793000000000000
  1: 0.3779000000000000
  0: 0.1237000000000000
  3: 0.1191000000000000
  mean = 1.4938

  var : p
  Probabilities:
  false: 0.8809000000000000
  true: 0.1191000000000000
  mean = [false = 0.8809,true = 0.1191]


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  Coin   = [0,1],
  Sample = resample(3,Coin),
  Heads  = count_occurrences(1,Sample),
  P      = check(Heads == 3),
  add("heads",Heads),
  add("p",P).


/*
  Another approach

  var : heads
  Probabilities:
  2: 0.3774000000000000
  1: 0.3677000000000000
  3: 0.1291000000000000
  0: 0.1258000000000000
  mean = 1.5098

  var : p
  Probabilities:
  false: 0.8709000000000000
  true: 0.1291000000000000
  mean = [false = 0.8709,true = 0.1291]

*/
go2 ?=>
  reset_store,
  run_model(10_000,$model2,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go2 => true.
  
  
model2() =>
  Throws = bern_n(1/2,3),
  Heads  = Throws.sum,
  P      = check(Heads == 3),
  add("heads",Heads),
  add("p",P).