USE OF TABLES. 81 



The odds are a to >, for A against B, and n (a + 6) 

 trials are contemplated. Though we have only instanced 

 whole values of n, yet it may be a fraction : thus, if the 

 odds are 3 to 2, and 96 trials are contemplated, n (3 -f 2) 

 must be 9&? or n must be 191. In this case, the pro- 

 bable mean is that A shall happen 57|? and B 38 J- ; by 

 which it must be understood^ that a person who should 

 repeat Q6 throws a great many times, receiving 1 L for 

 every A, would, in the long run, gain on the average 

 57f /. per trial of 96 throws. 



The square root in question, represented algebrai- 

 cally, is 



or the square root of the product of S, n, a, and 6 di- 

 vided by a -f- & I now subjoin the two principal pro- 

 blems, with the two rules in parallel columns. 



PROBLEM. What is the chance that the number of 

 As in w(a-f-&) trials shall lie between na -f / and 

 na I, both inclusive ? or what is the chance that the 

 departure from the probable mean shall not exceed / ? 



BY TABLE I. BY TABLE II. 



Find the square root, and 

 divide one more than twice I 

 by it ; call the result t, and 

 find H answering to t in the 

 table. (Use the rule in p. 70. 

 if necessary.) This H is the 

 probability required. 



Find the square root, and 

 multiply it by 31 ; then divide 

 by 130. To I add -5, and 

 divide by the preceding 

 quotient ; call the result t, 

 and find the value of K 

 answering to t : this is the 

 probability required. 



N. B. The neutral departure 



j is -5 less than the quotient first 



I found. 



PROBLEM. What is that degree of departure within 

 which it is p to q that the number of As in n (a + b) 

 trials shall lie ? 



