All arrangemets are equally likely, but the probability is, of course, zero. So with probability one you don't get only zeros.
There is a theorem that says that any finite arbitrary configuration will appear an infinite number of times in an infinite random sequence with probability one. Saibal Neil Lion wrote: > > It's undefinable. You're just as likely to get all zeros, > or all ones, as you are to get any arrangement of numbers you care to > mention (or can mention); the probability being 0 for each, I suppose. The > difference is, there are some infinite binary strings of numbers you cannot > define without an infinite description (semantic paradoxs > aside).. which one assumes, are 'truly' random. > > >From: Norman Samish <[EMAIL PROTECTED]> > >To: [EMAIL PROTECTED] > >Subject: The infinite list of random numbers > >Date: Thu, 08 Nov 2001 20:41:30 -0800 > > > >Suppose an ideal random number generator produces, every microsecond, > >either > >a zero or a one and records it on a tape. After a long time interval one > >would expect the tape to contain a random mix of zeroes and ones with the > >number of zeroes equal to the number of ones. Is this necessarily true? > >Is > >it possible that, even after an infinite time had passed, that the tape > >could > >contain all zeroes or all ones? Or MUST the tape contain an equal number > >of > >zeroes and ones? Why? If you have a reference dealing with this topic, > >please let me know. Thanks, > >Norm Samish > > > _________________________________________________________________ > Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp >
