of Edinburgh, Session 1878-79. 
Ill 
tively. The probability that if the cause present itself, an event 
E will accompany it (whether as a consequence of the cause A x or 
not) is p v and the probability that if the cause A 2 present itself, 
that event E will accompany it, whether as a consequence of it or 
not, is q. Moreover, the event E cannot appear in the absence of 
both the causes, A x and A 2 . Required the probability of the 
event E. 
The data are — 
x = a , y — b , xz — ap , yz — bq> 
and 
(1 - x)(l - y)z = 0, 
and z is required. 
ISTow (1 - #)(1 - y)z = z - xz - yz + xyz , 
z = xz +yz - xyz 
by the last datum ; 
z < xz + yz - x - yz + 1 . . (1.) 
< xz + yz - y - xz + 1 . . (2.) 
< xz + yz . . . . . (3.) 
. z < 1 - a + ap . . . . (1.) 
<T -b+bq- ■ ■ ■ (2.) 
< ap + bq. . . . (3.) 
Also 
(1 - x)yz — yz - xyz , 
= yz + z - xz - yz 
by the last datum ; 
.-. z = xz + ( 1 - x)yz ; 
.'. z> ap. 
Also 
z >bq* 
This problem was discussed in the “ Philosophical Magazine,” 
by Boole, Wilbraham, and Cayley. Cayley’s solution is different, 
applying to a modification of the problem. Boole goes further, and 
finds the most probable value of the probability. "Wilbraham con- 
siders only mathematical probability, and maintains, quite rightly, 
that we cannot proceed further than above without making assump- 
tions. He says that the disadvantage of Boole’s method is,, that it 
does not show whether a problem is determinate. This desideratum 
is supplied by the method of indeterminate coefficients to which I 
have referred above. 
VOL, x. 
Q 
