xxxviii Tables for Statisticians and Biometricians [III 



Here - - may be obtained from Table II, or if xi be very large from Schlomilch' 



formula, i.e. 



1 (I _ a x ) 1 / 1 1 5 



I ~~" * / O c\ \ "i / 



+ 



+ 4) K 2 + 2)( 1 2 + 4)( 1 2 + 6) 

 9 129 



; + 2 ) (x 2 + 4) (a* 2 + 6) (! 2 + 8) (x? + 2) (xj 2 + 4) (i 2 + 6) (x-f + 8) (^ 2 + 10) 

 57 \ .. 



Table III will suffice for approximate results. 



Illustration (v). ; 



A. bag contains 360 balls, of which one-third are white and two-thirds black. 

 What is the chance of drawing at least 45 white balls when we extract 90 balls at 

 a single drawing ? 



If a bag contains n balls, pn white and qn black, the probability when we 

 draw r balls that at least r t will be white is equal to the first + 1 terms of 

 the series 



pn (pn - 1) ... ( pn - r + 1) 

 n(n l)...(w r+1) 



/_ r nq r(r 1) nq(2q 1) \ , ... N 



V ( 1 -I i 1 5 '- 1 \ V / I \ f Vlll} 



V l!pn-r+l n r!2! (pn-r + 1) (pn -r + 2) ^ ) 

 But this is a hypergeometrical series for which 



a = r, (3 = nq, <y=pn r + l, and n = ry a /3-I. 

 In our special case 



pi=120, gn = 240, $ = 45, r = 90, 

 and we need the first 46 terms of the series (ii) for 



a = -90, /3 = -240, 7 = 8! (ix). 



m u t becomes 



7(7 + !). ..i 



r(7) 





