276 LIGHT SCIENCE FOR LEISURE HOURS. 



are three balls in a bag, one being white, the others 

 black. Then, if we draw a ball at random, it is clear 

 that we are twice as likely to draw a black as to draw 

 a white ball. This is technically expressed by saying 

 that the odds are 2 to 1 against drawing a white ball ; 

 or 2 to 1 071 (that is, in favour of) drawing a black 

 ball. This being understood, it follows that, when the 

 odds are said to be 2 to 1 against a certain horse, we 

 are to infer that, in the opinion of those who have 

 studied the performance of the horse, and compared 

 it with that of the other horses engaged in the race, 

 his chance of winning is equivalent to the chance of 

 drawing one particular ball out of a bag of three 

 balls. 



Observe how this result is obtained : the odds are 2 

 to 1, and the chance of the horse is as that of drawing 

 one ball out of a bag of three three being the sum of 

 the two numbers 2 and 1. This is the method followed 

 in all such cases. Thus, if the odds against a horse 

 are 7 to 1, we infer that the cognoscenti consider his 

 chance equal to that of drawing one particular ball out 

 of a bag of eight. 



A similar treatment applies when the odds are not 

 given as so many to one. Thus, if the odds against a 

 horse are as 5 to 2, we infer that the horse's chance 

 is equal to that of drawing a white ball out of a bag 

 containing five black and two white balls or seven 

 in all. 



We must notice also that the number of balls may 

 be increased to any extent, provided the proportion 



