86 ESSA5T ON PROBABILITIES. 



presumption that the chance of A lies between - and 



a-j-6 

 a+k 



or that the odds for A against B lie hetween a to b 



and a + k to b k. But in this case, |H V is 

 the presumption that the chance of A lies between 

 a k a 



- - and - or that the odds for A against B lie 

 a + b a + b' 



between a k to b + k and a to b. 



But if A have happened most times,, make -JH -f V 

 and |H V change places in the preceding paragraph, 

 every thing else remaining the same. 



EXAMPLE. In a thousand trials, A has happened 

 600 times, and B 400 times. What is the pre- 

 sumption," 1. that the odds for A against B lie 

 between 600 to 400 and 630 to 370 ; 2. that the 

 odds for A against B lie between 570 to 430 and 600 

 to 400 ? 



From the preceding problem t=l'369., say = 1*37; 

 the square root is 21'91, and H is '9471. 



t = l-S7A17036 1-12844 6-a = 200 



JA2 232 -17268 



- - 3000x21-91=65730 

 H'= -17268 -95576 



200 



65730)191 -152(-0029 =V 



4765 =JH + V 

 4707=JH-V 



Hence (since A has happened most times), it is "4707 

 to *5293, or about 47 to 53, that the odds for A against 

 B lie between 600 to 400 and 630 to 370. And it is 

 4765 to -5235, or about 48 to 52, that the odds for A 

 against B lie between 570 to 430 and 600 to 400. 



The problems which the preceding part of this 

 chapter has enabled us to solve, are the determination 

 of the chance which exists (under known circumstances) 

 for the happening of an event a number of times which 



