The Doctrine of Chances: Or, a Method of Calculating the Probabilities of Events in Play. The Third Edition, Fuller, Clearer, and More Correct Than the Former. By A. de Moivre, ...A. Millar, 1756 - 348 pages |
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Page 3
... value of the Sum expected by the Fraction which represents the Probability of obtaining it . Thus , if I have 3 Chances in 5 to obtain 100 L. I say that the present value of my Expectation is the product of 100 L by the frac- tion , and ...
... value of the Sum expected by the Fraction which represents the Probability of obtaining it . Thus , if I have 3 Chances in 5 to obtain 100 L. I say that the present value of my Expectation is the product of 100 L by the frac- tion , and ...
Page 271
... Value of the Reverfion . SOLUTION . Let M be the Value of the Life in Poffeffion , r the Rate of In- terest , then the present Value will be — M , that is , from the Value of the Perpetuity , fubtract the Value of the Life in Poffeffion ...
... Value of the Reverfion . SOLUTION . Let M be the Value of the Life in Poffeffion , r the Rate of In- terest , then the present Value will be — M , that is , from the Value of the Perpetuity , fubtract the Value of the Life in Poffeffion ...
Page 272
... present Problem , if B dies before A , the Heirs of B have no Expectation . SOLUTION . Let M be the Value of the Life of the present Poffeffor , P the Value of the Life of the Expectant , then the Value of his Expecta- tion is P - MP ...
... present Problem , if B dies before A , the Heirs of B have no Expectation . SOLUTION . Let M be the Value of the Life of the present Poffeffor , P the Value of the Life of the Expectant , then the Value of his Expecta- tion is P - MP ...
Page 274
... Value of the Life of C , fubtract the half Sum of the Values of himself and A , and of himself and B ; then to the ... Present Value is M ' " ' , which Symbol we make ufe of to reprefent the Prefent Value of an Annuity upon three equal ...
... Value of the Life of C , fubtract the half Sum of the Values of himself and A , and of himself and B ; then to the ... Present Value is M ' " ' , which Symbol we make ufe of to reprefent the Prefent Value of an Annuity upon three equal ...
Page 275
... Value of that Expectation ? SOLUTION . I - d A d A Make 3 M " - 2 M " A , let the Intereft of 1 1. be = d , then the present Value of that Expectation will be xp . But to know the Intervals of Time after which the Lives will be filled ...
... Value of that Expectation ? SOLUTION . I - d A d A Make 3 M " - 2 M " A , let the Intereft of 1 1. be = d , then the present Value of that Expectation will be xp . But to know the Intervals of Time after which the Lives will be filled ...
Other editions - View all
The Doctrine of Chances: Or, a Method of Calculating the Probabilities of ... Abraham De Moivre No preview available - 2017 |
The Doctrine of Chances: Or, a Method of Calculating the Probabilities of ... Abraham de Moivre No preview available - 2015 |
The Doctrine of Chances: Or, a Method of Calculating the Probabilities of ... Abraham De Moivre No preview available - 2018 |
Common terms and phrases
affigned againſt alfo alſo Annuity anſwer bability becauſe Binomial Bowls Cafe Cards Chances for taking Chances for winning Chances whereby circumftance Coefficients confequently confideration COROLLARY denoted Dice divided Doctrine of Chances eafily equal Equation Expectation exprefs the number exprefs the Probability faid fame manner fecond feveral fhall fhew fhould fince fingle firft Term firſt follows fome four throws Fraction fubtracted from Unity fuch fuppofed Gain Gamefters given number happening Intereft laft laſt likewife lofing Lofs Logarithm loſe multiplied muſt Nicolas Bernoulli number of Chances number of Games number of Stakes number of Terms obferved Odds Play Ponte prefent Value Probabilities of winning Probability of taking Probability of throwing Probability required Problem Product Progreffion proportion Purchaſe Quotient raiſed Ratio reaſon refpectively remaining reprefent Series ſhall SOLUTION ſuppoſe Table taken thefe theſe thofe thoſe Trumps uſe wherefore whereof whofe whole number
Popular passages
Page 226 - The sum of the products of the roots taken two and two, with their respective signs, is equal to the co-efficient of the third term.
Page xi - The Author of this Work, by the failure of his Eye-sight in extreme old age, was obliged to entrust the Care of a new Edition of it to one of his Friends; to whom he gave a Copy of the former, with some marginal Corrections and Additions, in his own hand writing.
Page 209 - Terms next following as have been taken already, but prefix to them in an inverted order, the Coefficients of the preceding Terms. But if d be an even number, take so many Terms of the said Power as there are Units in...
Page 1 - 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.
Page 4 - ... it is the product of the sum adventured, multiplied by the loss. What is called advantage or disadvantage in play, results from the combination of the several expectations of the gamesters, and of their several risks. Thus, supposing A and B play together, and that A has deposited 51. and B 31., and that the number of chances which A has to win is 4, and the number of chances B has to win 2, and that it were required to determine the advantage or disadvantage of the players, we may reason thus...
Page 263 - Rules that might eafily be applied to the Valuation of feveral Lives; which, however, was happily overcome, the Rules being fo eafy, that by the Help of them, more can be performed in a Quarter of an Hour, than by any Method before extant , in a Quarter of a Tear.
Page 38 - ... and the product 3'5 will show that there is more than an equality of chance in four tickets for one or more prizes, but less than an equality in three. REMARKS. In a lottery whereof the blanks are to the prizes as 39 to 1, if the number of tickets in all were but 40, the proportion above mentioned would be altered, for 20 tickets would be a sufficient number for the just expectation of a single prize. Again, if the number of tickets in all were 80, still preserving the proportion of 39 blanks...
Page 251 - As, upon the Supposition of a certain determinate Law according to which any Event is to happen, we demonstrate that the Ratio of Happenings will continually approach to that Law, as the Experiments or Observations are multiplied : so, conversely, if from numberless Observations we find the Ratio of the Events to converge to a determinate quantity, as to the Ratio of P to Q,', then we conclude that this Ratio expresses the determinate Law according to which the Event is to happen.
Page 263 - Tears; it appears, that Life is carried to 90, 95, and even to 100 Years ; I am no more moved by it, than by the Examples of Parr or Jenkins, the firft of whom lived 152 Tears, and the other 167.
Page 252 - Events would converge to no fixt Ratio at all. Again, as it is thus demonstrable that there are, in the constitution of things, certain Laws according to which Events happen, it is no less evident from Observation, that those Laws serve to wise, useful and beneficent purposes; to preserve the stedfast...