On the Solutions of Questions in the Theory of Probabilities, 91 



relative — ^that there ia not and cannot be any kind of pre-emi- 

 nence among events founded merely upon the mode of their 

 expression. The neglect of this consideration makes truth to be 

 not merely the creature of language, but the creature of the 

 merest accidents of language. 



The paper which I forward on the Conditions by which the 

 Solutions of Questions in the Theory of Probabilities are limited, 

 will be followed, should circumstances permit, by two others ; 

 one containing a statement of the principles upon which my 

 method is founded, the other an analysis of its results considered 

 especially with reference to the question of the conditions of limi- 

 tation. It was my design to publish all these researches in a 

 single memoir. I have now determined to send them forth at 

 once, in the hope that when I shall have calmly stated my views, 

 I may with propriety leave the further discussion of them to 

 others. 



I am. Gentlemen, 



Your most obedient Servant, 



Lincoln, July 5, 1854. George Boole. 



XIII. On the Conditions by which the Solutions of Questions in the 

 Theory of Probabilities are limited. By George Boole, LL.D,, 

 Professor of Mathematics in Queen^s College, Cork^, 



SUPPOSE the following question in the theory of probabili- 

 ties to be given : " The probability that it rains on a given 

 day is p, the probability that it both rains and hails is q ; required 

 the probability w that it neither rains nor hails/^ We know that 

 the data of this problem cannot represent a possible experience 

 unless p is equal to or greater than q. The absolute probability 

 of an event " rain," cannot be less than the probability of the 

 joint occurrence of that event and of another event 'Hiail." 

 Again, we know that the probability w which we have to seek 

 cannot exceed 1 —p. The probability that it neither rains nor 

 hails cannot exceed the probability that it does not rain. Hence 

 the data of the problem are limited by the condition 



and the probability sought, viz. w, by the condition 



w^l —p. 



If the former condition is not satisfied in the data, the problem 

 is not a real one. If the latter is not satisfied in the solution, 

 that solution may at once be pronounced to be incorrect. Con- 

 ditions of this nature are involved in almost every problem on 



* Communicated by the Author. 



