Simulation of statistic riddle

[Former Member]

I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?

You can read the article with the riddle here: Hype about conditional probability puzzles

The riddle was also mentioned this week on SPON: DE Das Geschwister-Problem

As normal there is a lot of discussion in the article comments about the solution 13/27.

So just proof the solution with a simulation.

1. Create 1.000.000 families with two children {m,f} 50:50 and born on {sa,su,mo,tu,we,th,fr} 1:7


2. Count chance, that family has two boys 1/4


3. Count chance, that family has two boys, if you know that one child is a boy 1/3


4. Count chance, that family has two boys, if you know that one child is a boy and born on tuesday 13/27

If you program it, it is obvious, that each additional information (one child is a boy, one child is a boy born on tuesday) changes the sample for the probability calculation.

Simple ABAP program

  CONSTANTS:

    c_female    TYPE i VALUE 0,

    c_male      TYPE i VALUE 1,

    c_saturday  TYPE i VALUE 0,

    c_sunday    TYPE i VALUE 1,

    c_monday    TYPE i VALUE 2,

    c_tuesday   TYPE i VALUE 3,

    c_wednesday TYPE i VALUE 4,

    c_thursday  TYPE i VALUE 5,

    c_friday    TYPE i VALUE 6.



  TYPES:

    BEGIN OF ys_family,

      child1_gender          TYPE i,

      child1_day_of_the_week TYPE i,

      child2_gender          TYPE i,

      child2_day_of_the_week TYPE i,

    END OF ys_family.



  DATA:

    lo_rnd    TYPE REF TO cl_random_number,

    ls_family TYPE ys_family,

    lt_family TYPE TABLE OF ys_family,

    li_won    TYPE i,

    li_lost   TYPE i,

    li_total  TYPE i.



  CREATE OBJECT lo_rnd.

  CALL METHOD lo_rnd->if_random_number~init.



  DO 1000000 TIMES.



    ls_family-child1_gender = lo_rnd->if_random_number~get_random_int( 1 ).

    ls_family-child1_day_of_the_week = lo_rnd->if_random_number~get_random_int( 6 ).

    ls_family-child2_gender = lo_rnd->if_random_number~get_random_int( 1 ).

    ls_family-child2_day_of_the_week = lo_rnd->if_random_number~get_random_int( 6 ).

    APPEND ls_family TO lt_family.



  ENDDO.



  WRITE: / 'Chance to have two male children'.

  CLEAR: li_won, li_lost.

  LOOP AT lt_family INTO ls_family.

    ADD 1 TO li_total.

    IF ls_family-child1_gender EQ c_male AND

       ls_family-child2_gender EQ c_male.

      ADD 1 TO li_won.

    ELSE.

      ADD 1 TO li_lost.

    ENDIF.

  ENDLOOP.

  WRITE: / 'total', li_total, 'Won:', li_won, 'Lost:', li_lost.

  li_won = li_won * 100 / li_total.

  li_lost = li_lost * 100 / li_total.

  li_total = li_total * 100 / li_total.

  WRITE: / 'total', li_total, '%', 'Won:', li_won, '%', 'Lost:', li_lost, '%'.



  ULINE.



  WRITE: / 'Chance to have two male children, if you know that first child is male'.

  CLEAR: li_won, li_lost.

  LOOP AT lt_family INTO ls_family.

    IF ls_family-child1_gender EQ c_male OR

       ls_family-child2_gender EQ c_male.

      ADD 1 TO li_total.

      IF ls_family-child1_gender EQ c_male AND

         ls_family-child2_gender EQ c_male.



        ADD 1 TO li_won.

      ELSE.

        ADD 1 TO li_lost.

      ENDIF.

    ENDIF.

  ENDLOOP.

  WRITE: / 'total', li_total, 'Won:', li_won, 'Lost:', li_lost.

  li_won = li_won * 100 / li_total.

  li_lost = li_lost * 100 / li_total.

  li_total = li_total * 100 / li_total.

  WRITE: / 'total', li_total, '%', 'Won:', li_won, '%', 'Lost:', li_lost, '%'.



  ULINE.



  WRITE: / 'Chance to have two male children, if you know that first child is male and born on tuesday'.

  CLEAR: li_won, li_lost.

  LOOP AT lt_family INTO ls_family.

    IF ls_family-child1_gender EQ c_male OR

       ls_family-child2_gender EQ c_male.

      IF ( ls_family-child1_gender EQ c_male AND

           ls_family-child1_day_of_the_week EQ c_tuesday ) OR

         ( ls_family-child2_gender EQ c_male AND

           ls_family-child2_day_of_the_week EQ c_tuesday ).

        ADD 1 TO li_total.

        IF ls_family-child1_gender EQ c_male AND

           ls_family-child2_gender EQ c_male.

          ADD 1 TO li_won.

        ELSE.

          ADD 1 TO li_lost.

        ENDIF.

      ENDIF.

    ENDIF.

  ENDLOOP.

  WRITE: / 'total', li_total, 'Won:', li_won, 'Lost:', li_lost.

  li_won = li_won * 100 / li_total.

  li_lost = li_lost * 100 / li_total.

  li_total = li_total * 100 / li_total.

  WRITE: / 'total', li_total, '%', 'Won:', li_won, '%', 'Lost:', li_lost, '%'.

Output example

Chance to have two male children

 total 1.000.000 Won: 250.442 Lost: 749.558

 total 100 % Won: 25 % Lost: 75 %



Chance to have two male children, if you know that first child is male

 total 750.485 Won: 250.442 Lost: 499.943

 total 100 % Won: 33 % Lost: 67 %



Chance to have two male children, if you know that first child is male and born on Tuesday

 total 138.231 Won: 66.430 Lost: 71.701

 total 100 % Won: 48 % Lost: 52 %