The Gaming Table by Andrew Steinmetz, Volume II
The Doctrine Of Probabilities Applied To Gambling
The probability of an event is greater or less according to the
number of chances by which it may happen, compared with the whole
number of chances by which it may either happen or fail.
Wherefore, if we constitute a fraction whereof the numerator be
the number of chances whereby an event may happen, and the
denominator the number of all the chances whereby it may either
happen or fail, that fraction will be a proper designation of the
probability of happening. Thus, if an event has 3 chances to
happen, and 2 to fail, then the fraction 3/5 will fairly
represent the probability of its happening, and may be taken to
be the measure of it.
The same may be said of the probability of failing, which will
likewise be measured by a fraction whose numerator is the number
of chances whereby it may fail, and the denominator the whole
number of chances both for its happening and failing; thus the
probability of the failing of that event which has 2 chances to
fail and 3 to happen will be measured by the fraction 2/5.
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