/* 

  Random ratio in Picat.

  https://brainstellar.com/puzzles/probability/112
  """
  p and q are two points chosen at random between 0 & 1. What is the probability 
  that the ratio p/q lies between 1 & 2?

  Answer: 0.25
  """

  Cf my Gamble model gamble_random_ratio.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 : ratio
  Probabilities (truncated):
  120604.116999928621226: 0.0001000000000000
  2964.735349504506758: 0.0001000000000000
  1783.696794799288455: 0.0001000000000000
  1622.089267188111762: 0.0001000000000000
  .........
  0.000609779562723: 0.0001000000000000
  0.000542087201848: 0.0001000000000000
  0.000344019189895: 0.0001000000000000
  0.000330871599078: 0.0001000000000000
  mean = 16.6596
  HPD intervals:
  HPD interval (0.94): 0.00033087159908..8.71964436536633

  var : prob
  Probabilities:
  false: 0.7529000000000000
  true: 0.2471000000000000
  mean = [false = 0.7529,true = 0.2471]
  HPD intervals:
  show_hpd_intervals: data is not numeric


*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean,show_hpd_intervals,
                           hpd_intervals=[0.94]]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  P = beta_dist(1,1),
  Q = beta_dist(1,1),

  Ratio = P / Q,

  Prob = check( (Ratio >= 1, Ratio <= 2)),
  
  add("ratio",Ratio),
  add("prob",Prob).