USE OF TABLES. 77 



RULE. Divide one more than twice I by the square 

 root already mentioned, and the quotient being made 

 t, the value of H in Table I. is the probability re- 

 quired. 



EXAMPLE I. In 6000 throws with a die, what is 

 the chance that the number of aces shall not differ from 

 1000 by more than 50; that is, shall lie between 950 

 and 1050, both inclusive. Here a = 1, 6 5, 

 n = 1 000, 1 50, and the square root as before is 8 1 *65. 

 Divide 2 /+ 1. or 101, by 81'65, which gives 1*237, 

 which being t, H is '91977. Hence it is 920 to 80 in 

 favour of the proposed event, or about 11^ to 1 . 



EXAMPLE II. In 200 tosses, what is the chance that 

 the number of heads shall lie between 97 and 103, both 

 inclusive ? Here a = 1, 6 = 1, n = 100, I = 3, and 

 the square root, as before, is 20. And 2 / + 1, or 7, 

 divided by 20, gives '35, which being t, H is -379. 

 Hence it is 621 to 379. or about 31 to 19, against the 

 proposed event. 



EXAMPLE III. In 12 tosses, what is the chance of 

 the heads being either 5, 6, or 7 in number ? Here 

 a =. 1, 6 = 1, n =. 6, / = 1, and the square root, as 

 before, is 4'9- And 2 I -{- 1, or 3, divided by 4*9, gives 

 6l, which being t, H is *6ll7- Hence it is about b'l 2 

 to 388, or 153 to 97, in favour of the proposed event, 

 In page 47 the chance of this event is 



792 + 924 + 792 2508 



or or '612 



4096 4096 



PROBLEM IV. The odds for A against B being a to 6, 

 and n times a -j- b trials being to be made, for what 

 number is there a given probability H that the As shall 

 not differ from the probable mean by more than that 

 number ? 



RULE. Find in Table I. the value of t answering to 

 that of H (page 71), multiply it by the square root 

 already described, subtract 1, and divide by 2 : the 



