/* 

  Left some candles in Picat.

  https://brainstellar.com/puzzles/probability/216
  """
  You are taking out candies one by one from a jar that has 10 red candies, 
  20 blue candies, and 30 green candies in it. What is the probability 
  that there is at least 1 blue candy and 1 green candy left in the jar when 
  you have taken out all the red candies?

  Assume that the candies of the same color are indistinguishable from one another.
  
  Answer: 7/12 0.583333
  """

  Cf https://math.stackexchange.com/questions/1805078/candies-withdrawal-probability-for-a-particular-subsequence

  Cf my Gamble model gamble_left_some_candles.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.

main => go.

/*

  var : num blue
  Probabilities (truncated):
  0: 0.3373000000000000
  1: 0.2281000000000000
  2: 0.1543000000000000
  3: 0.1042000000000000
  .........
  12: 0.0008000000000000
  13: 0.0005000000000000
  15: 0.0003000000000000
  14: 0.0002000000000000
  mean = 1.8131

  var : p blue
  Probabilities:
  true: 0.6627000000000000
  false: 0.3373000000000000
  mean = [true = 0.6627,false = 0.3373]

  var : num green
  Probabilities (truncated):
  0: 0.2497000000000000
  1: 0.1987000000000000
  2: 0.1475000000000000
  3: 0.1115000000000000
  .........
  20: 0.0003000000000000
  22: 0.0001000000000000
  21: 0.0001000000000000
  19: 0.0001000000000000
  mean = 2.6872

  var : p green
  Probabilities:
  true: 0.7503000000000000
  false: 0.2497000000000000
  mean = [true = 0.7503,false = 0.2497]

  var : p
  Probabilities:
  true: 0.5833000000000000
  false: 0.4167000000000000
  mean = [true = 0.5833,false = 0.4167]

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  

f(A) = Res =>
  if not member(red,A) then
    Res = A
  else
    Res = f(A.tail)
  end.
model() =>
  Candles = ones(10,red) ++ ones(20,blue) ++ ones(30,green),

  S = draw_without_replacement(Candles.len,Candles),

  A = f(S),

  NumBlue = count_occurrences(blue,A),
  PBlue = check(NumBlue > 0),
  NumGreen = count_occurrences(green,A),
  PGreen = check(NumGreen > 0),
  P = check((PBlue,PGreen)),
  
  add("num blue",NumBlue),
  add("p blue",PBlue),  
  add("num green",NumGreen),
  add("p green",PGreen),
  add("p",P).