104 NOTE ON A QUESTION IN THE THEORY OF PROBABILITIES. [121 
The sense of the terms being clearly understood, the problem presents of course 
no difficulty. Let A. be the probability that the cause A acting will act efficaciously; 
g the probability that the cause B acting will act efficaciously; then 
jt? = A + (1 — A) p,(3, 
q = /x + (1 - a\, 
which determine A, g; and the total probability p of the effect is given by 
p = Xa + p,(3 — XpLCcfi; 
suppose, for instance, a=l, then 
p = X -f- (1 — A.) g/3, q — pj -f- A — XpL, p = X + p/3 — Ap>/3, 
that is, p = p, for p is in this case the probability that (acting a cause which is 
certain to act) the effect will happen, or what is the same thing, p is the probability 
that the effect will happen. 
Machynlleth, August 16, 1853.