of Edinburgh, Session 1878-79. 
Cor. 3. Suppose that A n always speaks falsely, then 
- PiPr-JPn-i) • 
109 
Cor. 4. Suppose that any other than A,, always speaks falsely, 
then 
0 . 
X * O' 
that is, the probability is quite indefinite. 
Cor. 5. Suppose that each p = i , 
then, 
-sKo-cr> 
which, when n is infinite is equal to jj , that is, is perfectly in- 
definite. 
(4.) A goes to hall p times in q consecutive days and sees B 
there r times. What is the most probable number of times that B 
was in the hall in the q days'? — Whitworth's Choice and Chance. 
U = the consecutive days ; 
x = on which A goes to hall ; 
y = on which B goes to hall. 
The data are — 
Tjx — p ; 
. \ by means of the theorem, 
U = q 
U xy = r j 
Cy = r + ^(q - p) 
To find the most probable value, make the assumption of inde- 
pendence, that is, that B is as likely to go to hall when A does not 
go, as when A does go. 
Then the most probable value of Uy is 
r + -(< i - p) = r -*L . 
P ' P 
Whitworth gives 
( q + 1 )r 
or next lower integer. 
Cor. Let r = p = q. Then IT y = q. 
VOL. x 
p 
