Starting a web site - Each of the ten digits 0 through 9
Each of the ten digits 0 through 9 will occur about & of the time in a (uniform) sequence of random digits. Each pair of two successive digits should occur about & of the time, etc. Yet if we take a truly random sequence of a million digits, it will not always have exactly 100,000 zeros, 100,000 ones, etc. In fact, chances of this are quite slim; a sequence of such sequences will have this character on the average. Any specified sequence of a million digits is equally as probable as the sequence consisting of a million zeros. Thus, if we are choosing a million digits at random and if the first 999,999 of them happen to come out to be zero, the chance that the final digit is zero is still exactly &, in a truly random situation. These statements seem paradoxical to many people, but there is really no contradiction involved. There are several ways to formulate decent abstract definitions of random- ness, and we will return to this interesting subject in Section 3.5; but for the moment, let us content ourselves with an intuitive understanding of the concept. At first, people who needed random numbers in their scientific work would draw balls out of a well-stirred urn or would roll dice or deal out cards. A table of over 40,000 random digits, taken at random from census reports, was published in 1927 by L. H. C. Tippett. Since then, a number of devices have been built to generate random numbers mechanically; the first such machine was used in 1939 by M. G. Kendall and B. Babington-Smith to produce a table of 100,000 random digits, and in 1955 the RAND Corporation published a widely used table of a million random digits obtained with the help of another special