116 Probability 



ratio if he uses the formula a = '}/2\/n, which is algebraically the 

 same since p = 3^n and q = 3^n. By this method the calcula- 

 tion of the previous problem becomes: 



^ = y^-y^n = Yi ' 10.54 = 5.27 



This formula can be used only for a 1 : 1 ratio. 



Ratios other than 1 : 1 may also be tested by this method. 

 Let us examine a possible 3 : 1 ratio. In Nemesia strumosa a 

 common type of flower has white lips whereas a less common but 

 very attractive type has a margin of blue around all the upper 

 lips of the corolla. This blue-margin type is found in plants 

 homozygous for bm, a recessive gene, whereas the white type that 

 lacks the blue margin has the dominant allele, Bm. Two white- 

 flowered plants were crossed and the progeny segregated into 86 

 white and 23 blue-margin. Is this ratio a true example of a 3 : 1 

 ratio? If so, it must be presumed that both white-flowered 

 parents were heterozygous. Let us find it by the percentage 

 method : 



a 



= J^/.^/^ZiX:o;?5= 4.15 per cent 

 \ n \ 109 



d 3*9 per cent 



- = = 0.94 



or 4.15 per cent 



With 109 plants, the standard error for a 3 : 1 ratio is 4.15 per 

 cent whereas the deviation was only 3.90 per cent. It is safe, 

 then, to assume that this ratio is a true example of a 3 : 1 ratio. 



As for the 1 : 1 ratio, calculations of standard errors of 3 : 1 

 ratios may often be simplified by the use of a special formula de- 

 rived from the general formula which can be applied only to a 



3 : 1 ratio. This formula is o- = ^ . When we apply this to 

 our case in Nemesia, we have: 



V37i V327 18.08 



or = = = = 4.52 



4 4 4 



