The fractions which represent the probabilities of happening and
failing, being added together, their sum will always be equal to
unity, since the sum of their numerators will be equal to their
common denominator. Now, it being a certainty that an event will
either happen or fail, it follows that certainty, which may be
conceived under the notion of an infinitely great degree of
probability, is fitly represented by unity.
These things will be easily apprehended if it be considered that
the word probability includes a double idea; first, of the number
of chances whereby an event may happen; secondly, of the number
of chances whereby it may either happen or fail. If I say that I
have three chances to win any sum of money, it is impossible from
the bare assertion to judge whether I am likely to obtain it; but
if I add that the number of chances either to obtain it or miss
it, is five in all, from this will ensue a comparison between the
chances that are for and against me, whereby a true judgment will
be formed of my probability of success; whence it necessarily
follows that it is the comparative magnitude of the number of
chances to happen, in respect of the whole number of chances
either to happen or to fail, which is the true measure of
probability.
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