Archive image from page 459 of The cyclopaedia; or, Universal dictionary. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature cyclopaediaoruni07rees Year: 1819 DOCTRINE OF CHANCES. See and the ferics P + p + 2 9-9- ' â â¢â¢' ./â ind q are very large numbers, it will be i pof- fib'e t > apply tins rule to practice on account of ti ' l â zEa'l' greater than S + i+iEa>l' + Etf I but in all cafes, where z is fmall, and alfo where the difparity be- fween/ and q is not great, the chance is very nearly = 2 2. In this rule, it is to be obferved, that (fuppofing m' =
Archive image from page 459 of The cyclopaedia; or, Universal dictionary. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature cyclopaediaoruni07rees Year: 1819 DOCTRINE OF CHANCES. See and the ferics P + p + 2 9-9- ' â â¢â¢' ./â ind q are very large numbers, it will be i pof- fib'e t > apply tins rule to practice on account of ti ' l â zEa'l' greater than S + i+iEa>l' + Etf I but in all cafes, where z is fmall, and alfo where the difparity be- fween/ and q is not great, the chance is very nearly = 2 2. In this rule, it is to be obferved, that (fuppofing m' = , K = the ratio of the quadrantal arc of a circle to its apq radius, and H = the ratio, whofe hyp. log. aâ i 26 â i 2â i 360 ri' 1260 ri 16S0 ri 4- &c.) S is made = in n + 1 V2 pq r,.-. , , â Hn VK n X £-a X E cf V> into the fenes x â n + 1 Vz I â¢- 2 m z' â+ z n + â &c. andEJ' = n + + +'a' â v n ~ââ,== multiplied iato the ratio, 2 VKpq v whofe hyp. log. is â x 12 n p q 3 C i 260 f i08» ri> f a> kc. 1183 ri' p q> From the preceding investigation, it appears that the fir ft rule gives a direct and perfect folution in all cafes, and that the f'.cond rule is only a method of approximating to the fo- lution, when the labour of applying the firft rule becomes too great, if either/ or q are nothing, or very fmall, it is evident that the firft rule gives an eafy correct folution; but, in all r cafes, recourfe mull I, had to the approxi- mation in the fecond rule; which, however, may be gene- rally computed without any great diffii .1 v. Indeed, what principally recommends the folution d this propofition is, that giving complete information whencith q- Suppofmg an event to have happened abort the pro- bability of which nothing further is known than that it has happened once, and that it be inquired what conchilion fhould be drawn from hence with refpect to the probability of its happening on a tr
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