/* 

  Pepperoni pizza in Picat.

  From Statistics101 (Resampling Stats)
  File pepperoniPizza.txt
  """
  If 24 pieces of sausage are randomly put onto a pizza that is sliced
  into 8 pieces (with none of the sausage pieces getting cut), what is the
  probability that your slice will have 3 pieces of sausage?
  From: "Statistics the Easy Way" Downing & Clark, 3rd edition, p. 58.
  -> 
  probability: 0.2412
  probability: 0.2338
  probability: 0.239532
  """


  Cf my Gamble model gamble_pepperoni_pizza.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:
  3: 0.2395000000000000
  2: 0.2269000000000000
  4: 0.1753000000000000
  1: 0.1398000000000000
  5: 0.1056000000000000
  6: 0.0464000000000000
  0: 0.0421000000000000
  7: 0.0172000000000000
  8: 0.0062000000000000
  9: 0.0009000000000000
  10: 0.0001000000000000
  mean = 2.9988

  var : p
  Probabilities:
  false: 0.7605000000000000
  true: 0.2395000000000000
  mean = 0.2395

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs,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() =>
  NumPieces = 24,
  NumSlices = 8,

  % Place 24 pieces of sausage (randomly) on the 8 slices
  Pizza = resample(NumPieces,1..NumSlices),

  % How many sausages are on my slice (slice 1)?
  C = count_occurrences(1,Pizza),

  P = check(C == 3), %  Did I get 3 sausages?
  
  add("c",C),
  add("p",P).