48 ESSAY ON PROBABILITIES. 



of combinations of 1,2,3., &c. out of 24, we have the 

 following summary : 



H T 24 and H 24 T happen in 1 case each. 



H 12 T 12 happens in 2704156 cases. 

 The odds are now about 6 to 1 against the even di- 

 vision of the pieces into heads and tails. But let us 

 consider the same degree of departure from the most 

 probable case as we took before. An alteration in one 

 piece out of twelve answers to that of 2 pieces out of 

 24. Now the number of cases in which either HIO 



arrives, and the odds of one or other of them, is com- 

 puted as follows : 



H 10 T 14 or H 14 T 10 3922512 16777216 whole No. of cases 

 H n T 13 or H 13 T n 4992288 11618956 No. favourable 

 H 6 T 6 2704156 - 



- 5158260 No. unfavourable 

 11618956 



or it is now more than 2 to 1 in favour of the heads 

 lying between 10 and 14, both inclusive. 



I now put together the principles on which we have 

 hitherto gone, adding two more, the first of which 

 (Principle III.) is obviously a consequence of the pre- 

 ceding, and the second of which will be presently ex- 

 plained. 



Principle I. When all the ways in which an event 

 may happen are equally probable, the chance of its 

 happening is the number of ways in which it may 

 happen, divided by all the number of ways in which it 

 may happen and fail. 



