/* 

  Mr Shearer's class in Picat.

  https://minerva-demo.github.io/#category=Probability&index=2
  """
  Question
  Three-fourths of the students in Mr. Shearer's class have brown hair and six-sevenths 
  of his students are right-handed. If Mr. Shearer's class has 28 students, what is the 
  smallest possible number of students that could be both right-handed and have brown hair?
  ...
  Reference answer
  Mr. Shearer has 3/4(28)=21 students with brown hair and 6/7(28)=24 students who are 
  right-handed. Since there are 28−24=4 left-handed students, at most 4 of the 
  21 brown-haired students are left-handed. Therefore, at least 17 of them are 
  right-handed. Final Answer: The final answer is 17.
  ...
  Problem source: MATH Counting & Probability Level 1
  """


  Cf my Gamble model gamble_mr_shearers_class.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 both
  Probabilities:
  18: 0.4730000000000000
  17: 0.2960000000000000
  19: 0.1920000000000000
  20: 0.0380000000000000
  21: 0.0010000000000000
  mean = 17.975

  numBoth = [18 = 0.473,17 = 0.296,19 = 0.192,20 = 0.038,21 = 0.001]
  min_value = 17


*/
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=false
                          ]),
  nl,
  NumBoth = get_store().get("num both").get_probs,
  println(numBoth=NumBoth),
  println(min_value=min(NumBoth).first),
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  NumStudents = 28,

  % 3/4 of the class has brown hair
  HasBrownHair = bern_n(3/4,NumStudents),
  % Enforce this
  observe( HasBrownHair.sum * 4 == 3 * NumStudents ),

  % 6/7 of the class are right handed
  IsRightHanded = bern_n(6/7,NumStudents),
  % Enforce this
  observe( IsRightHanded.sum * 7 == 6 * NumStudents ),

  % How many has both brown hair and are right handed?
  NumBoth = [cond( (HasBrownHair[S]==1,IsRightHanded[S]==1),1,0) : S in 1..NumStudents].sum,

  if observed_ok then
    add("num both",NumBoth)
  end.