304 LIGHT SCIENCE FOR LEISURE HOURS. 



One propounds to his neighbor the following ques- 

 tion : " I say, Charley, if the odds are 2 to 1 against 

 Rataplan, and 4 to 1 against Quick March, what's 

 the betting about the pair ? " " Don't know, I'm sure," 

 replies Charley; "but I'll give you 6 to 1 against 

 them." The absurdity of the reply is, of course, very 

 obvious; we see at once that the odds cannot be 

 heavier against a pair of horses than against either 

 singly. Still there are many who would not find it 

 easy to give a correct reply to the question. What 

 has been said above, however, will enable us at once 

 to determine the just odds in this or any similar case. 

 Thus -the odds against one horse being 2 to 1, his 

 chance of winning is equal to that of drawing one 

 white ball out of a bag of three, one only of which is 

 white. In like manner, the chance of the second horse 

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

 of five, one only of which is white. Now we have to 

 find a number w r hich is a multiple of both the numbers 

 three and five. Fifteen is such a number. The chance 

 of the first horse, modified according to the principle 

 explained above, is equal to that of drawing a white 

 ball out of a bag of fifteen of which fne are white. In 

 like manner, the chance of the second is equal to that 

 of drawing a white ball out of a bag of fifteen of which 

 three are white. Therefore, the chance that one of 

 the two will win is equal to that of drawing a white 

 ball out of a bag of fifteen balls of which eight (five 



