/* 

  Four girls and one boy in Picat.

  From Statistics101
  """
  What is probability of selecting 4 girls and 1 boy,
  in any order, when selecting five students from any 
  25 girls and 25 boys? 
  (From Page 122ff in "Resampling Stats: The New Statistics").
  """

  Exact probability:
  Picat> X=hypergeometric_dist_pdf(5, 25, 50, 4)
  X = 0.149261832392533

  ChatGPT-o1-preview get the same result:
  https://chatgpt.com/share/66f3ad34-4d20-800b-a760-7f05c5f525fb
  """
  Thought for 30 seconds
  ...
  Answer: An exact probability of 1375 divided by 9212, that is, 
  probability = 1375⁄/9212 (~ 0.149261832392531)
  """


  Cf my Gamble model gamble_four_girls_and_one_boy.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 : num girls
  Probabilities:
  2: 0.3319000000000000
  3: 0.3233000000000000
  4: 0.1495000000000000
  1: 0.1445000000000000
  5: 0.0268000000000000
  0: 0.0240000000000000
  mean = 2.5102

  var : p
  Probabilities:
  false: 0.8505000000000000
  true: 0.1495000000000000
  mean = [false = 0.8505,true = 0.1495]


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  N = 25, % N boys and N girls
  M = 5,  % pick M children

  Children = ones(N,boy) ++ ones(N,girl),
  Selected = draw_without_replacement(M, Children),

  % How many girls?
  NumGirls = count_occurrences(girl,Selected),
  
  % 4 girls?
  P = check(NumGirls == 4),

  add("num girls",NumGirls),
  add("p",P).



/*
  A simpler model

  var : num girls
  Probabilities:
  3: 0.3260000000000000
  2: 0.3070000000000000
  1: 0.1690000000000000
  4: 0.1490000000000000
  0: 0.0300000000000000
  5: 0.0190000000000000
  mean = 2.452

  var : p
  Probabilities:
  false: 0.8510000000000000
  true: 0.1490000000000000
  mean = [false = 0.851,true = 0.149]


*/
go2 ?=>
  reset_store,
  run_model(10_000,$model2,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go2 => true.
  
  
model2() =>
  % 50 children. boys = 0, girls = 1
  D = bern_n(1/2,50),

  % Pick 5. How many girls?
  NumGirls = take(D,5).sum,
  
  % 4 girls?
  P = check(NumGirls == 4),

  add("num girls",NumGirls),
  add("p",P).