/* 

  How many sons? in Picat.

  From Ruma Falk:
  "Understanding Probability and Statistics - A Book of Problems"
  page 56

  """
  How many sons?

  Mrs. F is known to be the mother of two. You meet her in town
  with a boy whom she introduces as her son. What is the probability
  that Mrs. F has two sons? One possible is that the probability 
  is 1/2: you now have seen one boy, and there the question is 
  whether the other child is a male. Another possibility is that
  the probability is 1/3: you learned that Mrs. F has 'at least
  one boy', and hence three equiprobable family structures are
  possible (BB, BG, GB), of which the target event (BB) is but one.
  Which is the correct answer? Explain.

  (Hint: What are your assuptions about the chance mechanism that
  yielded your observation of Mrs. F hand her son?)
  """

  This problem (with a slighly different wording) was also in
  Maya Bar-Hillel & Ruma Falk: "Some teasers concerning conditional
  probabilities" (Cognition 11, 1982, page 109-122).


  Here we show these two different approaches:
  - model1: p(two_sons) = 1/2
  - model2: p(two_sons) = 1/3

  As commented in the hint (and the comments at page 177), the 
  assumptions regarding the "chance mechanism" - i.e. how we 
  know what - matters.

  Cf my Gamble model gamble_how_many_sons.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.

/*
  Model 1

  In this model we know that the "first child" is a son.

  var : child1
  Probabilities:
  son: 1.0000000000000000
  mean = [son = 1.0]

  var : child2
  Probabilities:
  daughter: 0.5025257627803597
  son: 0.4974742372196403
  mean = [daughter = 0.502526,son = 0.497474]

  var : child2 == son?
  Probabilities:
  false: 0.5025257627803597
  true: 0.4974742372196403
  mean = [false = 0.502526,true = 0.497474]


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

  [Child1,Child2] = uniform_draw_n(G,2),

  observe(Child1 == son),
   
  if observed_ok then
    add("child1",Child1),
    add("child2",Child2),
    add("child2 == son?",check(Child2 == son)),    
  end.


/*
  In this model we only know that one of the children
  - but not which of them - is a son.

  var : children
  Probabilities:
  [son,daughter]: 0.3370696557245796
  [son,son]: 0.3333333333333333
  [daughter,son]: 0.3295970109420870
  mean = [[son,daughter] = 0.33707,[son,son] = 0.333333,[daughter,son] = 0.329597]

  var : num sons
  Probabilities:
  1: 0.6666666666666666
  2: 0.3333333333333333
  mean = 1.33333

  var : num sons == 2
  Probabilities:
  false: 0.6666666666666666
  true: 0.3333333333333333
  mean = [false = 0.666667,true = 0.333333]


*/
go2 ?=>
  reset_store,
  run_model(10_000,$model2,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,
  % fail,
  nl.
go2 => true.
  
  
model2() =>
  G = [son,daughter],

  % The gender of of two children
  Children = uniform_draw_n(G,2),

  % How many of the childrens are sons?
  NumSons = [cond(C==son,1,0) : C in Children].sum,

  % We know that at least one of the children is a son
  observe(NumSons >= 1),
   
  if observed_ok then
    add("num sons",NumSons),
    add("children",Children),
    add("num sons == 2",check(NumSons == 2)),    
  end.