Hoyle's Games, Improved And Enlarged - online book

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( 4 )
The object of the calculation of probabilities is to discover facts, the reality of which is un­known to us.
The probability of an event may be said to be more or less, according to the number of chances by wrhich it may happen, compared with the whole number of chances by which it may either happen or fail.
If we, therefore, 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 happen or fail, that fraction will be the proper designation of the probability of the event. Thus, if an event has 3 chances to happen and 2 to fail, the fraction $ will fitly represent the probability of its happen­ing, and may be said 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 by which it may fail, and the denominator the whole number of chances for and against, as -?-.
Thus the number of the two fractions represent-ing the probability of the advent or not of an event is equal to unity. When one, therefore, is given, the other may be found by subtraction.
The expectation, that is, the sum which the person who has a chance for the advent of an event is entitled to, if he resign his chance to an­other, is always the product of the fraction repre-
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