## An Essay on Probabilities, and Their Application to Life Contingencies and Insurance Offices |

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alive allowed amount annuity answer appears applied average bank become begin calculation called Carlisle cent chance circumstances common Consequently consideration considered contains continuance correct death depends divided drawing drawn equal error event example existence favour fluctuation former fraction gain give given greater happen increase individual instance insurance office interest joint known latter less limits lives loss lottery mathematical mean method mortality multiply namely nearly necessary negative observations paid party payment perpetuity persons play player positive possible preceding premiums present value principles probability problem produce profit proportion question reason receive remaining result risk ruin rule square root stake successive sufficient suppose supposition surplus term theory thing throws trials true truth white ball whole

### Popular passages

Page 226 - I/, to be received at the end of the year in which the life fails (the year being supposed to commence with the.

Page 214 - What is the value of 11., to be received at the end of the year in which a life of 30 shall fail ? Perpetuity of £l at 3 per cent.

Page xxix - Find 933, the present value of £1 to be received at the end of the year in which A dies, provided he die while B is living.

Page 27 - What prospect," are his own words, " would there have been of such a concurrence of circumstances, if a state of chance had been the only antecedent ? With regard to the sameness of the directions, either of which might have been from west to east, or from east to west, the case is precisely similar to the following : There is a lottery containing black and white balls, from each drawing of which it is as likely a black ball shall arise as a white one : what is the chance of drawing eleven balls...

Page 239 - He might also invest the interest, and thus obtain compound interest: but it is not easy for an individual to do this. Unless he provide an agent to draw the dividends immediately on their becoming due, various circumstances will happen to prevent the immediate investment of the interest. It is not at all an unfair calculation to suppose that, upon each half-yearly dividend, a month will be lost, so that nominal compound interest for 42 years will only be really for 35 years.

Page 99 - H appeared at the first toss; in 494, at the second; in 232, at the third; in 137, at the fourth ; in 56, at the fifth ; in 29, at the sixth ; in 25, at the seventh ; in 8, at the eighth ; and in 6, at the ninth. Let us, then, compute the amount which he would have received if he had bond fide played all these games on the preceding terms. 1061 x 2 = 2122^ 494 x 4 = 1976 232 x 8 = 1856 137 x 16 = 2192 56 x 32 = 1792 29 x 64 = 1856 25 x 128 = 3200 8 x 256 = 2048 6 x 512 = 3072 The 2048 games would...

Page 42 - The common error attached to this problem is, that since there are six faces, it is most likely all will have come up in six throws.

Page 305 - ... strong presumptive evidence one way or the other. This comparison was accordingly made, and the agreement between the distribution of the several coins in the bag and those in the box was such as to leave no doubt as to the former having formed a part of the latter.

Page 217 - Take the rate of interest which money really makes *, and subtract the premium for 11. from the present value of 1 /. to be received at the end of a year (see last table) : divide the remainder by the excess of unity over the remainder, and the quotient is the number of years- purchase in the present value of the annuity.

Page 245 - This action is, in point of law, founded upon a supposed damnification of the plaintiffs, occasioned by his death, existing and continuing to exist at the time of the action brought : and being so founded, it follows of course, that if, before the action was brought, the damage, which was at first supposed likely to result to the creditors from the death of Mr. Pitt...