BIOMETRY 



And it is clear that any one of these combinations is 

 equally likely to appear on any given occasion, if the 

 coins are supposed to be strictly symmetrical, and are 

 tossed up entirely at random. Now, the second and 

 third results are the same unless the two coins are indi- 

 vidually distinguishable. So we may write the most 

 likely result of tossing up two pennies four times in the 

 following way : 



i HH + zHT + iTT. 



And in a similar way we may discover that the most 

 likely result of tossing up three coins eight times is : 



i HHH + sHHT + sHTT + iTTT. 



In the first case H T is twice as likely to appear as 

 H H at any single throw, and in the second case H H T 

 is three times as likely as H H H in any single toss. 



It is possible to work out the most probable relative 

 frequency of the various possible combinations in the 

 case of any number of coins. Thus for ten coins the 

 sequence of numbers runs : 



TABLE II. 



