USE OF TABLES. 



EXAMPLE 1. When t is 1-56. what is H'> 

 A= 9745 



*A2 = 151 



/ H'= -09896 



EXAMPLE 2. When t z= 1-23412, what is H' ? 

 t=l-23 H'= -24852 



,_ 

 t=l-24 H'=- 24245 ' 6 7 



412 -24852 



607 250 



2884 Subt. -24602:=H' when t= 1-23412 



2472 



250,084 



We have already seen that when two events, A and 

 B, one of which must happen at every trial, have 

 severally happened m times and n times in m + n 

 trials, it is m -f 1 to n -f 1 that A shall happen 

 at the next trial. But m + 1 to n -f 1 is very 

 nearly m to n, when m and n are considerable num- 

 bers: for instance, 248 to 11? is very nearly 247 to 

 116. That is, when a great many trials have been 

 made, the numbers of times which A and B have hap- 

 pened express very nearly the odds (relative proba- 

 bilities) for A against B ; or, inverted, for B against A. 

 Let us convert the problem, and supposing that we 

 know beforehand the chances of A and B, are we to 

 suppose that in a great many trials A and B will happen 

 in proportion to their respective probabilities ? Common 

 sense tells us that such will always be nearly the case, 

 but that the odds are great against an. exact result. 

 Suppose 3000 drawings to be made from a lottery con- 

 taining two As and one B. We must then, it seems 

 clear, draw A twice as often as B, in the long run. 

 Our reason convinces us thus. Let one of the As be 

 distinguished from the other by an accent, so that we 

 have A, A', and B. If the urn be well shaken before 

 each drawing, it is impossible to believe that, in the 



