348 PROF. W. STANLEY JEVONS ON 



statement is r. What is the probability that if they agree 

 in a statement, their statement is true?"*' 



This is solved in the simplest possible manner. Let 



a= prob. of A and B both speaking trnth. 

 y8= prob. of A but not B j, „ 



7= prob. of not A but B ,, ,, 



S = prob. of neither A nor B „ „ 



Then we have the following data : — 



Prob. of A speaking truth =a-\-l3=p. 



„ „ B „ „ =a-\-r^=q. 



Prob. that they disagree =z^-\-ty=r. 



As it is certain that one or other of the alternatives must 

 happen, we have the condition 



a + /S + 7 + S=l. 



These four equations are sufficient to determine all the 

 four unknown quantities by ordinary algebra. Thus 



a , 



8= I - (a+/3 + 7) = I -^±^-r, 



2 



Now the probability required is, that if A and B agree in 

 a statement their statement is true. By the principles of 



probability this is ^ ; and inserting the above values of 



a and 8 we have 



a _p+q—r 



a + S 2(l-r)' 



which is the same as the result which Boole obtained in a 

 much more complicated manner. This verifies the an- 

 ticipations both of Boole himself (p. 281) and of Mr. 



