» ON PROBABILITY.
io which are possible, but who disregards them by reason of their reputed
improbability, is perhaps what is meant. Some philosophers have
r endeavoured to fix the numerical fraction to which this moral certainty is
equal by observing the risks of which men are in general careless. Buffon
a chose the fraction 4%%% ; Condorcet estimated it in a different manner, and
— of course obtained a very different result. Indeed it is obvious that this
TH fraction is arbitrary, and we shall therefore not enter more minutely into
Tatio of (he this question. There may, perhaps, be a practical utility for each man to
chanees by determine the risk his own temperament enables him to disregard, in order
'e must he to obtain a standard with which to compare the results of occasional
[ lef such theorems: without some such comparison they might fail in their abstract
Dressions numerical form to determine his judgment.
ended fo 9. We have said that probability does not exist in the abstract, but always
® went in refers to the knowledge possessed by some particular individual. Let us
suppose that a bag contains one white and two black balls, and that A
dy oe a having drawn a white ball holds it so that he can see what colour it is, but
5: att so that B cannot. Here three cases appear possible to B, of which two
at ip favour the drawing a black ball ; the probability therefore that it is a black
ra ball to B is 2, while the probability to A that it is a white ball, is unity, or
i certainty, Again: suppose a bag contain one white, one black, and one
red ball; A, having drawn a white ball, whispers to B that the ball which
” is drawn is not red. Three cases appear equally possible to C, of which
- one only favours the drawing a white ball ; C therefore estimates thé pro-
rent under bability at 1, while B (if he believes the information given him by A) has
only two alternatives to choose between: he therefore estimates the proba-
Buenced he bility at 4+ Even if B do not implicitly believe the information given him by
ubied t A, it is clear that his judgment will be formed on grounds different from
ie furnishes those on which C decides.
Degiectmg 10. It is thus that the same fact related before a numerous audience
ppiying to obtains from different individuals different degrees of belief: this is chiefly
Oi Measure to be attributed to the different degrees of knowledge possessed by different
urbe, the individuals of circumstances which bear on the fact in question. An inha-
Certainty, bitant of the torrid zone has difficulty in believing that water freezes; and
ty; 1 must the recovery of a sick person may appear probable to one unacquainted with
have called medicine, while the skilful physician despairs of effecting a cure. :
dil in the 11. It follows from the definition of probability, that to determine the
£ two words probability of any event, it is only necessary to enumerate the cases which
ral of the are favourable and those which are unfavourable to its production, in order
git Conse: to form the fraction which expresses its probability. In order that this may
be well understood, we shall begin with some very simple examples, and for
ty of draw- these it will be necessary, at first, to have recourse to games of chance, in
contain 10 which the whole number of possible occurrences js most readily ascertained.
| is dd, or Ex. 1. Suppose a piece of money is thrown into the air, and that the pro-
Jf draving bability of its falling on the obverse side twice successively is required : here
b its limits the following cases present themselves.
ag ve Case i The obverse both times.
i 2 The obverse the first time and the reverse the second.
} . The reverse the first time and the obverse the second.
very im* 4. The reverse both times,
thro These are the only cases possible ; and if we are ignorant of the existence
Ja of any cause tending to make the piece fall on one side rather than on the
* other, they are all similarly circumstanced, and therefore the probability of
. each case is 1.
B 2
