78 ESSAY ON PROBABILITIES. 



quotient, or its nearest whole number, is the answer 

 required. 



EXAMPLE. In 6000 throws with a die, within 

 what limits is it two to one that the aces shall be con- 

 tained ? The square root is 81 '65, and H is -| or '66667, 

 to which the value of t is -68409, found as follows 



(page 71): - 



H= -66667 

 Nearest below -66378 t=68 



Tab. Diff. 706) 289000(409 t= -68409 say -6841 

 2824 81-65 



6600 34205 



6354 41046 



. 6841 



246 54728 



2)54-86 



Answer. It is a little more than 2 to 1, that the 

 aces shall lie between 1000 - 28 and 1000 + 28, and 

 a little less than 2 to 1 that they shall lie between 

 1000 27 and 1000 + 27. 



But the most convenient way of solving this problem 

 is by first finding for what degree of departure from the 

 probable mean there is an even chance. In this case, 

 since H = -5 (page 70), t is =. '476936, which the 

 method in page 41, will show to be very nearly |^. It 

 will be worth while to re- state the whole process. 



The odds for A against B being a to 6, and the pro - 

 posed number of trials being n times a -f fe, required 

 the limits of departure from the probable mean na, 

 within which it is an even chance that the number of 

 As shall be contained. 



RULE. Multiply together 8,71,0, and 6, and divide by 



