Elements of Logick: Or, a Summary of the General Principles And Different ...
Elements of Logick: Or, a Summary of the General Principles And Different ...
Levi Hedge
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Hence ^e general rule 9* - Digitized by CjOOQIC 102 CALCULATION OF CHANCES is^ that the probability or improhahilUy of anf event is^ as the number of the favourable chances, divided by the sum of all the chances^ both fa- wu^^hh and unfavourable. 138. The degree of probability^ that any eyent will or will not happen^ is convepie^ntly expressed by a fraction^ whose numerator. rep- resents the number of chances^ which favour the existence^ or the nonexistence of the event ; ^aiul whose denominato...r is the sum of all the chances^ both favourable and adverse to the event. • Thus^ if an event have five chances to happen and three to fail^ the fraction -|* will ex- press the probability of its happening^ and the fraction |^, that of its failure. These two frac- tions^ which represent all the chances both of happening and failing, being added together^ their sum will always be equal to unity ; since the sum of their numerators will be just equal to their common denominator. And as in every case it is certain^ that an event will either hap- pen or.fail^ it follows^ that certainty is justly represented by unity.
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