/* 

  Daughter or son in Picat.

  From https://brainstellar.com/puzzles/probability/25
  """
  Sheldon says "Suppose I have two children. Younger one is a girl". What is 
  the probability that both children are girls?

  "Forget all that, and suppose I have two children, and atleast one of them 
  is a boy". Find probability of two boys.

  "Suppose I have two kids, lets call them Bouba and Kiki", says Dr. Cooper, 
  "and suppose Bouba is a girl !" What is the probability that I have two daughters?"
  """

  (Note: The Answer states 1/2, 1/3, 1/3 but in the Solution, the third
  is stated to be 1/2. See Comments on this.)


  Cf 
  - ppl_two_children_problem.pi
  - ppl_how_many_sons.pi
  - my Gamble model gamble_daughter_or_son.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.

/*
  """
  Sheldon says "Suppose I have two children. Younger one is a girl". What is 
  the probability that both children are girls?
  """

  var : child1
  Probabilities:
  girl: 0.7256972111553784
  boy: 0.2743027888446215
  mean = [girl = 0.725697,boy = 0.274303]

  var : child2
  Probabilities:
  girl: 0.7760956175298804
  boy: 0.2239043824701195
  mean = [girl = 0.776096,boy = 0.223904]

  var : youngest
  Probabilities:
  girl: 1.0000000000000000
  mean = [girl = 1.0]

  var : p
  Probabilities:
  true: 0.5017928286852590
  false: 0.4982071713147410
  mean = [true = 0.501793,false = 0.498207]

  I.e. the probability that both children are girls (p) is 1/2.

*/
go ?=>
  reset_store,
  run_model(10_000,$model,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go => true.
  
  
model() =>
  N = 2,
  Gender = [condt(flip(1/2),boy,girl) : _ in 1..N],
  Age = [ random_integer(10) : _ in 1..N],

  Child1 = Gender[1],
  Child2 = Gender[2],

  Age1 = Age[1],
  Age2 = Age[2],

  Youngest = cond(Age1 < Age2,Child1,Child2),

  P = check((Child1 == girl, Child2 == girl)),
  
  observe(Youngest == girl),
  
  if observed_ok then
    add("child1",Child1),
    add("child2",Child2),
    add("youngest",Youngest),
    add("p",P)
  end.


/*
  """
  "Forget all that, and suppose I have two children, and atleast one of them 
  is a boy". Find probability of two boys.
  """

  var : child1
  Probabilities:
  boy: 0.6775013376136971
  girl: 0.3224986623863028
  mean = [boy = 0.677501,girl = 0.322499]

  var : child2
  Probabilities:
  boy: 0.6508828250401284
  girl: 0.3491171749598716
  mean = [boy = 0.650883,girl = 0.349117]

  var : p
  Probabilities:
  false: 0.6716158373461745
  true: 0.3283841626538256
  mean = [false = 0.671616,true = 0.328384]

  The probability that both children are boys is 1/3.
*/
go2 ?=>
  reset_store,
  run_model(10_000,$model2,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go2 => true.
  
  
model2() =>
  N = 2,
  Gender = [condt(flip(1/2),boy,girl) : _ in 1..N],

  Child1 = Gender[1],
  Child2 = Gender[2],

  P = check((Child1 == boy, Child2 == boy)),
  
  observe( (Child1 == boy ; Child2 == boy) ),
  
  if observed_ok then
    add("child1",Child1),
    add("child2",Child2),
    add("p",P)
  end.


/*
  """
  "Suppose I have two kids, lets call them Bouba and Kiki", says Dr. Cooper, 
  "and suppose Bouba is a girl !" What is the probability that I have two daughters?"
  """

  var : bouba
  Probabilities:
  girl: 1.0000000000000000
  mean = [girl = 1.0]

  var : kiki
  Probabilities:
  boy: 0.5025927403270841
  girl: 0.4974072596729158
  mean = [boy = 0.502593,girl = 0.497407]

  var : p
  Probabilities:
  false: 0.5025927403270841
  true: 0.4974072596729158
  mean = [false = 0.502593,true = 0.497407]

  This case is the same as in case 1, i.e. probability (p) is 1/2.

  (Then fact that they was named by concrete names did not discern them further.)

*/
go3 ?=>
  reset_store,
  run_model(10_000,$model3,[show_probs_trunc,mean]),
  nl,
  % show_store_lengths,nl,
  % fail,
  nl.
go3 => true.
  
  
model3() =>
  N = 2,
  Gender = [condt(flip(1/2),boy,girl) : _ in 1..N],

  Bouba = Gender[1],
  Kiki = Gender[2],

  P = check((Bouba == girl, Kiki == girl)),
  
  observe(Bouba == girl),
  
  if observed_ok then
    add("bouba",Bouba),
    add("kiki",Kiki),
    add("p",P)
  end.