Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!linus!decvax!harpo!eagle!jerry
From: jerry@eagle.UUCP (Jerry Schwarz)
Newsgroups: net.math,net.misc,net.rec.bridge
Subject: Re: simple (?) statistics problem solved
Message-ID: <1075@eagle.UUCP>
Date: Tue, 23-Aug-83 04:21:41 EDT
Article-I.D.: eagle.1075
Posted: Tue Aug 23 04:21:41 1983
Date-Received: Tue, 23-Aug-83 15:38:38 EDT
References: <1814@rabbit.UUCP>, <903@utcsstat.UUCP> utcsstat.908
Lines: 56



This discussion has taken a typical course.  Each side 
repeats arguments in favor or one answer without addressing 
where the other side has gone wrong.  In this item I will
try to expose the error in Laura's reasoning.  

But first, it is possible to demonstrate that she
is wrong without finding a flaw in her reasoning by
conducting an experiment.  A program to simulate the 
conditions of the problem is attached below.
On our machine it gives the result:
	    n_gold=654, n_silver=346

So where is the flaw in her reasoning?  It is that her
idea of "rescanning" is not well formulated.  In order to
be correct the "rescan" must use ALL the knowledge acquired
by opening a drawer.  But, besides the certainty that
one cabinet is eliminated we have gained a certain amount
of information from having carried out a random trial.  
The experimental evidence shows that this information
must be taken into account.

The idea of gathering knowledge from random trials is a 
commonplace and intuitive one. Perhaps it is slightly obscured 
when, as in this problem, statistical information is combined 
with definite information.

Jerry Schwarz
eagle!jerry

/**************************************************************/
typedef enum { gold, silver } COIN ;

COIN drawers[6] = 
	{ silver, silver, silver, gold, gold, gold } ;

main() {
    int n_gold = 0 ;
    int n_silver = 0 ;
    int choice ;

    while ( n_gold+n_silver < 1000 ) {
	choice = (rand()>>5) % 6 ;
	switch  ( drawers[choice] ) {
	    case silver: /* ignore these trials */ break ;
	    case gold: {
		switch( drawers[ choice^1 ] ) {
		    case gold:   ++n_gold   ; break ;
		    case silver: ++n_silver ; break ;
		    } break ;
	        }
	    }
	}
    printf("n_gold=%d, n_silver=%d\n",n_gold,n_silver) ;
    }