ON PROBABILITY. 
1 (Ra 
—_ — Ri 2 2 
(3) +s irtess 2a} 
ry 3% de (CHV JIE IN, GED. 2 
2)" 2i+1 2.3 =): 3 
: 5 y 
which probability is greater than 6) , the result when the shilling is sup- 
posed homogeneous. 
Ex. 20. It follows, from what has preceded, that if an individual has 
made m + n assertions, of which m are true and 2 are false ; the probabi- 
: : : 1 
lity of his telling the truth, in any case, is Gh 
) # y Rr far as we draw 
our conclusions from these assertions alone, 
mol” Wile Ley ov: 
Let rats =v, and let p be the a priori probability of an event 
which he asserts to have taken place, 
The event observed is the assertion by this individual that the event took 
place, of which the a priori probability is p. 
If the event did take place, the individual tells the truth; the probability 
of the event on this hypothesis is pv. 
- The probability of the event on the contrary hypothesis is (1 — p) (1=v), 
therefore the probability of this hypothesis is 
pv 
p+ (1 ~p) A —2) 
po 1 
If tt, | 
- pot A-pa-o~ 73 
Thus we see that when a witness asserts that an event has taken place, 
he renders the probability that it did take place greater than the simple 
probability of the event only when his veracity is greater than 4, which result 
might have been foreseen. tru 
~ Ex. 21. A witness asserts that out of a bag containing a thousand 
tickets, a given ticket, say No. 70, has been drawn, required the probability bu 
that this number was drawn. 
. Let the veracity of the witness be v, as before. 
The event observed is the assertion by the witness that the given number 
was drawn, the probability of this event, on the hypothesis that the witness 
tells the truth, is TE the probability of the event on the contrary hypothe- 
wor Lr. 2999 i 
sis, namely, that this ticket wasnot drawn, is 1000 (1 —v); but if the witness 
is supposed to have no reason or inducement for choosing the No. 70 in 
preference to any other of the 999 undrawn numbers, this probability must 
1 : , : s : 
be multiplied by 999’ which is the probability of the witness choosing this 
number from the 999 undrawn numbers, so that the probability of the event 
: aa = pon gm fy 
on this hypothesis is 005" 
3.0.