USE OF TABLES. 85 



or, which is the same thing, that 



Probability of B lies between -- and 



a + b a+b 



For since it is our hypothesis, that either A or B must 

 happen at every trial, whatever presumption there is that 

 the chance of A is #, there is the same presumption that 

 the chance of B is 1 #. 



But we might ask the following questions : A and B 

 having happened a and b times in a + b trials, what are 

 the values of the following presumptions ? 



1. That the probability of A lies between and ; 



a + b a + b 



or its equivalent, that the probability of B lies between 

 b-k b 



; an <* T 



a + b a + b* 



2. That the probability of A lies between and , 



a+b a+b 



or that the probability of B lies between and - 



a+b a+b 



To solve these by the help of the following rule, 

 remember that, if a be greater than 6, it is more likely 

 that the chance of A falls short of a -4- (a -f 6) than ex- 

 ceeds it : and if a be less than b, then it is more likely 

 that the chance of A exceeds a-f-(a-|~6) than falls short 

 of it. 



RULE. First find the result of the preceding pro- 

 blem, and find from Table I. the H' (p. 72} belong- 

 ing to the value of t. Subtract this from the H / 

 derived from in the table (which is 1-12844); mul- 

 tiply by the difference between b and a, and divide by 

 the product of the square root used in the preceding 

 problem and three times the whole number of trials : 

 call the result V. To one half of the result of the 

 preceding problem add V ; and from it subtract V : and 

 call these results ^H + V and |H-V. 



Then, if B have happened most times, JH-f V is the 

 G 3 



