/* 

  A Machine Probability Puzzle in Picat.

  From Cole Frederick: "A Machine Probability Puzzle - Will it ever work?" 
  https://colefp.medium.com/a-machine-probability-puzzle-bbb46322f609
  """
  Here’s a simple puzzle to test your ability to think about probability.

  Imagine you have a machine that works on average every 2 days out of 3. 
  What is the probability that it will work for at least 4 of the next 5 days?
  """

  Cf my Gamble model gamble_machine_probability_puzzle.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, ppl_common_utils.
import util.
% import ordset.

main => go.

/*

  var : s
  Probabilities:
  4: 0.3338000000000000
  3: 0.3291000000000000
  2: 0.1646000000000000
  5: 0.1285000000000000
  1: 0.0406000000000000
  0: 0.0034000000000000
  mean = 3.3348

  var : p
  Probabilities:
  false: 0.5377000000000000
  true: 0.4623000000000000
  mean = 0.4623

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  nl.
go => true.
  
  
model() =>
  NumDays = 5,
  WorkingP = 2/3,

  Days = bern_n(WorkingP,NumDays),
  S = Days.sum,
  P = check(S >= 4),
  
  add("s",S),
  add("p",P).