4 GO HAYGAETH. 



n est pas derangee, n'a pas ponte au pliaraon, ni qu'il y ait dix-neuf a 

 parier centre un, que cet liomme est un joueur. 



This would be absurd, M. de la Roche says, and he asserts that 

 the reasoning given by Haygarth's friend is equally absurd. We 

 may remark that there must be some mistake in this note ; he has 

 put 19 to 1 for 1 to 19, and vice versa. And it is difficult to see how 

 Prevost and Lhuilier can commend this note ; for M. de la Roche 

 argues that the reasoning of Haygarth's friend is entirely absurd, 

 while they only find it slightly inaccurate. For Prevost and 

 Lhuilier proceed to calculate the chances according to Laplace's 



prmciple ; and they nnd them to be ^ , — — - , — — - , which, as 



they say, are nearly the same as the results obtained by Hay- 

 garth's friend. 



855. The second section is on the extent of the principle. The 

 memoir asserts that we have a conviction of the constancy of the 

 laws of nature, and that we rely on this constancy in our applica- 

 tion of the Theory of Probability ; and thus we reason in a vicious 

 circle if we pretend to apply the principle to questions respecting 

 the constancy of such laws. 



856. The third section is devoted to the comparison of some 

 results of the Theory of Probability with common sense notions. 



In the formula at the end of Art. 843 suppose 5 = 0; the for- 

 mula reduces to 



{p+ 1) (jP + 2) ... (p + r) 



(p+2+2) (;? + $ + 3) ... (^ + g + r + l) ' 



it is this result of which particular cases are considered in the 

 third section. The cases are such as according to the memoir lead 

 to conclusions coincident with the notions of common sense ; in 

 one case however this is not immediately obvious, and the memoir 

 says, Ceci donne I'explication d'une esp(^ce de paradoxe remarque 

 (sans I'expliquer) par M. De La Place ; and a reference is given to 

 Ecoles no7miaIes, Qimie cahier. We will give this case. Nothing is 

 known d, priori respecting a certain die ; it is observed on trial that 

 in five throws ace occurs twice and not-ace three times ; find the 

 probability that the next four throws will all give ace. Here 



