/* 

  Two children problem in Picat.

  https://robeastaway.com/blog/boy-girl
  """
  I have two children, at least one of whom is a boy.  
  What is the chance that the second child is also a boy?

  ...

  The classic, surprising answer is that the chance of a second 
  boy is 1/3, not 1/2 as most would expect.  Why?  Because if I 
  have two children, there is an equal chance that they will be 
  Boy-Boy, Boy-Girl, Girl-Boy or Girl-Girl.  There are three 
  equally likely combinations in which at least one child is 
  a boy (BB, BG and GB) and only in the first scenario is the 
  other child also a boy.
  """

  We assume the inital probability of a boy/girl as 0.5.

  Cf my Gamble model gamble_two_children_problem.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.

/*

  First model: 
  """
  I have two children, _at least one of whom_ is a boy.  
  What is the chance that the second child is also a boy?
  """

  var : child1
  Probabilities:
  boy: 0.6573593936976466
  girl: 0.3426406063023534
  mean = [boy = 0.657359,girl = 0.342641]

  var : child2
  Probabilities:
  boy: 0.6762398617205159
  girl: 0.3237601382794841
  mean = [boy = 0.67624,girl = 0.32376]

  var : num boys
  Probabilities:
  1: 0.6664007445818375
  2: 0.3335992554181625
  mean = 1.3336

  I.e. the probability that the other child is also a boy (i.e. two boys) is 1/3,

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  Children = categorical_n([1/2,1/2],[boy,girl],2),
  NumBoys = [ cond(C == boy,1,0) : C in Children].sum,
  % Note: it's important that we state the condition
  %       "at least one of whom is a boy"
  %       as something like this.
  observe(NumBoys >= 1),
  
  if observed_ok then
    add("child1",Children[1]),
    add("child2",Children[2]),
    add("num boys",NumBoys),
  end.

/*
  Second model:
  """
  I have two children, the eldest is a boy.  
  What is the chance that the second child is also a boy?
  """

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

  var : child2
  Probabilities:
  girl: 0.5084041922088195
  boy: 0.4915958077911806
  mean = [girl = 0.508404,boy = 0.491596]

  var : num boys
  Probabilities:
  1: 0.5084041922088195
  2: 0.4915958077911806
  mean = 1.4916

  Since we now know that child1 is a boy, it's a matter of chance (50%) 
  if the other child is also a boy.
  
  Note:
  In ppl_how_many_sons.pi I model the same problems, but with a 
  little different approach.

*/
go2 ?=>
  reset_store,
  run_model(10_000,$model2,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go2 => true.
  
  
model2() =>
  Children = categorical_n([1/2,1/2],[boy,girl],2),
  NumBoys = [ cond(C == boy,1,0) : C in Children].sum,

  % "The eldest is a boy"
  observe(Children[1] == boy),

  if observed_ok then
    add("child1",Children[1]),
    add("child2",Children[2]),
    add("num boys",NumBoys),
  end.