Documentation for BIRTHDAY.PRG

There is a famous problem in  probabilities which goes as follows:
'Given   several people in a room,   how many people must there be 
for a duplicate birthday to be likely?'.   Well, there could be as 
few as 2 or as many as 366.   Assuming a 365 day year, there could 
be  365  different  birthdays  but the  366th  person  MUST  be  a 
duplicate  of  one of the 365.   So a guess of 'about  180'  seems 
reasonable.  After all, that's a rough average of 2 and 366. 

Well,  the  astonishing answer is 'less than 23'!   I  wrote  this 
simulation  program  to see if the right answer  would  seem  more 
credible after seeing the simulation.   You be the judge.  I think 
the  rest of this would mean more if you stopped reading this  for 
now  and ran the program.   No instructions are needed.   Just  be 
sure  that  the .RSC file is on the same disk,  (or  in  the  same 
folder) as the .PRG;  and then double click on the program. If you 
are  using  a color monitor you may have to set it up  for  medium 
resolution using the 'set preferences...' from the desktop.

                            Background  
Many   books  on  probabilities  use  this  problem  as  a   vivid 
demonstration  of  how  our intuition fails us when  it  comes  to 
probabilities.  Many  instructors  demonstrate this  in  class  by 
having  the  students give their birthdate.  If the class  is  big 
enough and the instructor is lucky,  the students have one  sample 
indicating  that  the mathematical answer _might_  be  right.   Of 
course,  that's only one sample, thus this program.  I have run it 
many  times  and have seen as few as 2 people and as many  as  71.  
The result is different each time the program is run, of course. 

My   favorite  book  on  probabilities  is  'An  Introduction   to 
Probability  Theory and its Applications,  Volume I',  by  William 
Feller.  He discusses this problem several places in the book with 
the best introductory discussion starting on page 31. His analysis 
shows  that based on a 365 day year,  _if_ birthdays were  equally 
distributed  throughout  the  year,   that  on  the  average   the 
probability  of a duplicate birthday is greater than 0.5  with  23 
people  in the sample.   That analysis ignores leap year  and  the 
simulator program includes the effect of leap year so the  results 
will be slightly different. 

                           The program
The  program has been compiled with level 1.0 of Personal  Pascal.  
I  have included the source code for its possible tutorial  value.  
The  program makes calls on VDI which one does not see every  day.  
This  capability  is  not described in the  reference  manual  for 
either  version  1 or version 2;  but OSS did document  it  via  a 
public  domain  upload more than a year ago.   I would  guess  the 
upload  is  on  most of the national BBS's.  AES  calls  are  also 
possible with a similar approach but there are no samples in  this 
program. 


The  program was written and debugged on a monochrome monitor  and 
then  procedures  were  added  (notably  MyLine,   MyLine_To,  and 
MyDrawString) to convert it for a medium resolution color monitor.  
Some  other  changes were also required to  make  color  work.   I 
tested  it  with  OmniRes on a mono monitor and it  works  if  the 
system  is  put in medium resolution by  the  user.   The  program 
includes code to internally change from low to medium res but this 
does not work properly with OmniRes.   The graphics are offset  to 
the left and the full screen is not drawn.  My guess (and hope) is 
that this is a peculiarity of OmniRes.  Since the code was already 
in place that _should_ do the change I left it in.  I hope someone 
will post a message to me telling me what happens when you run the 
program from a low resolution starting environment.    My  address 
on Genie is M.L.HANSON.