560 



THE BELL SYSTEM TECHNICAL JOURNAL, ^L\ltCH 1957 



tion since there is an extra parameter to vary and the appropriate 

 tables for the normal approximation are not available. 



In the computation of these probabilities the least favorable con- 

 figuration 



P[i] = P*i] and p*2] = p[2] = piz] = 



Pik] 



(14) 



was used. It follows from Appendix II that if the probability of a correct 

 selection is at least P* when (14) holds, then it will also be at least P* 

 when 



Pm ^ pfi] and p*2] ^ pi2] ^ Pm ^ • • • ^ p 



[k] 



(15) 



For small values of n, exact calculations were carried out. A typical 

 exact calculation is shown in Appendix IV. The approximations used 

 for large ?i are given in Appendix III. 



I.OO 



0.90 



0.80 



0.70 



0.60 



P2* 0.50 



O40 



0.30 



O20 



0.10 



0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 



Fig. 17 — Illustration of the varying zones of indifference and the least favor- 

 able configuration for ^• = 4 and P* = 0.85. (For n ^ 5 the longest vertical segment 

 occurs at the point An where the abcissa and the ordinate are svmmetrical about 

 0.5) 



