/* 

  Bag of marbles in Picat.

  From https://x.com/madeofmistak3/status/1818764350724944062
  """
  I have a question. Exactly 1/5th of the people in a town have Beaver Fever . There are 
  two tests for Beaver Fever, TEST1 and TEST2. When a person goes to a doctor to test for 
  Beaver Fever, with probability 2/3 the doctor conducts TEST1 on him and with probability 
  1/3 the doctor conducts TEST2 on him. When TEST1 is done on a person, the outcome is as 
  follows: If the person has the disease, the result is positive with probability 3/4. If 
  the person does not have the disease, the result is positive with probability 1/4. When 
  TEST2 is done on a person, the outcome is as follows: If the person has the disease, 
  the result is positive with probability 1. If the person does not have the disease, the 
  result is positive with probability 1/2. A person is picked uniformly at random from 
  the town and is sent to a doctor to test for Beaver Fever. The result comes out 
  positive. What is the probability that the person has the disease? 
  """

  The problem is from
  http://allendowney.blogspot.com/2017/02/a-nice-bayes-theorem-problem-medical.html
 

  Enumerate (exact) from my Gamble model gamble_beaver_fever.rkt:
  (#f : 8/13 (0.6153846153846154))
  (#t : 5/13 (0.38461538461538464))


  This is a port of my Gamble model gamble_beaver_fever.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.

main => go.

/*
  This model:

  Probabilities:
  false: 0.6478903239548438
  true: 0.3521096760451562

*/
go ?=>
  reset_store,
  run_model(20_000,$model,[show_probs]),
  nl.
go => true.
  
model() =>
  Sick = flip(1/5),
  Positive = cond( flip(1/3) == true,
                   cond(Sick, flip(3/4), flip(1/4)), % Test 1
                        cond(Sick, true, flip(1/2))), % Test 2
  observe(Positive),                       
  if observed_ok then
    add("sick",Sick)
  end.