/* 

  Lottery in Picat.

  From Mathematica (BernoulliDistribution)
  """
  A lottery sells 10 tickets for $1 per ticket. Each time there 
  is only one winning ticket. A gambler has $5 to spend. Find his probability of 
  winning if he buys 5 tickets in 5 different lotteries:

  D = ProductDistribution((BernoulliDistribution(1/10), 5));
  Probability(1 <= x + y + u + v + w, (x, y, u, v, w) -> D)
  ->
  40951/100000 (0.40951)

  His probability of winning is greater if he buys 5 tickets in the same lottery:
  PDF(HypergeometricDistribution(5, 1, 10), 1)
  -> 1/2

  """


  Cf my Gamble model gamble_lottery.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 different lottieries
  Probabilities:
  false: 0.5907000000000000
  true: 0.4093000000000000
  mean = [false = 0.5907,true = 0.4093]

  var : p same lottery
  Probabilities:
  0: 0.5092000000000000
  1: 0.4908000000000000
  mean = 0.4908

  var : p same lottery1
  Probabilities:
  1: 0.5083000000000000
  0: 0.4917000000000000
  mean = 0.5083


  Picat> X = hypergeometric_dist_pdf(5,1,10,1)
  X = 0.500000000000004



*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean % ,
                           % show_percentiles,
                           % show_hpd_intervals,hpd_intervals=[0.94],
                           % show_histogram,
                           % min_accepted_samples=1000,show_accepted_samples=true
                          ]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  N = 5,

  Win = bern_n(1/10,N),

  PDifferentLotteries = check(1 <= Win.sum),
  PSameLottery        = hypergeometric_dist(5,1,10), % Mathematica compliant parameters
  PSameLottery1       = hypergeometric1_dist(1,10,1,5),  
  
  add("p different lottieries",PDifferentLotteries),
  add("p same lottery",PSameLottery),
  add("p same lottery1",PSameLottery1).