/* 

  Card draw problem in Picat.

  https://www.reddit.com/r/Probability/comments/1gbm4d0/card_draw_problem/
  """
  I have 100 unique cards. Lets call them card1, card2, card3... etc.
  If i draw 40 cards from the deck what is the chance of me having both card1 and card2 in my hand?
  I asked chatgpt and it said 3.8% but my gut feeling tells me thats way too low.
  Can somone help me out here or is it really 3.8%?
  """

  Cf my Gamble model gamble_card_draw_problem.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 : p
  Probabilities:
  false: 0.8420500000000000
  true: 0.1579500000000000
  mean = 0.15795

*/
go ?=>
  reset_store,
  run_model(20_000,$model,[show_probs_trunc,mean % ,
                           % show_simple_stats % ,
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.84,0.9,0.94,0.99,0.99999],
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  N = 100,
  M = 40,

  X = take(shuffle(1..N),M),
  P = cond((membchk(1,X), membchk(2,X)),true,false),
  add("p",P).