38 ESSAY ON PROBABILITIES. 



17 to 4-, or 4| to 1, against the advantage. If the con- 

 tingent gain were 2 11. the value of the chance would be 

 4/., as will hereafter be more fully shown. 



Of all the pairs which can be drawn, there are 



10 x 1 2 = 1 20 green and white. 10 x 9 -r- 2 = 45 both green. 

 12 x 14=168 white and red. 12 x ll-s-2 = 66 both white. 

 14 x 10= 140 red and green. 14 x 13 -f- 2 = 91 both red. 



The sum of these is 630,, as it should be. The reader 

 should explain to himself the reason of the difference 

 of process. The least probable case is both green, 

 the most probable white and red. Nothing is more 

 common than the idea that the event most likely to 

 happen, which is compounded of two or more events, is 

 a repetition of the event which is individually the most 

 probable. This is true of repetitions : red being most 

 probable, it is more probable that red should be repeat- 

 ed than that white should be repeated, or that green 

 should be repeated ; but that two white ones should be 

 drawn is not so probable as that a white and red should 

 be drawn. The drawing, whatever it Tnay be, is con- 

 sidered independently of succession and this makes an 

 important difference. If the balls were drawn succes- 

 sively, both red is more probable than white followed 

 by red, or than red followed by white, but not more 

 probable than the chance of one or other, which is the 

 preceding case. 



I here also take occasion to notice the common 

 error, that because an event is more probable than any 

 other, it is the one to be looked for. The question 

 ought to be, Is that event more probable than some one 

 or other out of all the other events which may happen ? 

 If ten persons engage in a competition, with an equal 

 chance of success, and if two of them, A and B, enter 

 into partnership, it is now more probable that the firm 

 of A and B will win than that C will win, or that D 

 will win, &c. But the chances against the firm are 

 still 8 to 2 or 4 to 1. If a hundred halfpence be 

 tossed up into the air, the result which is more probable 

 than any other, is 50 heads and 50 tails. But com- 

 mon sense will tell us that the chances of this result are 



