Arithmetic for High Schools; Containing the Elementary and the Higher Principles and Applications of the Science - Softcover
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Book may have numerous typos, missing text, images, or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1859. Excerpt: ... CHAPTER XIV. MATHEMATICAL PROBABILITIES, AND THEIR APPLICATION TO LIFE ANNUITIES AND LIFE INSURANCE. (251.) The Theory Of Probabilities has respect to events which may be regarded as equally contingent; and, in the sense here intended, A contingent event is one of a number of events, some only of which will certainly occur, while no reason can be perceived .why any one of them should occur rather than any other ; as when one person is to be taken, by lot, from a company consisting of five persons § Measure of Probability. (252.) The Probability of a contingent event is measured, and expressed, by the ratio of the number of chances favorable to that event to the whole number of chances favorable and un-favorable to the same event. Suppose that one person only is to be taken by lot from among Jive persons, represented by A, B, C, D, and E. The Probability that the lot will fall on any particular one of the five, as A, is expressed by J, since he has one chance in five. In like manner the Probability that the lot will fall on any other one, as B, is £, since each person has one chance in five. Opposite Probabilities. i (253.) The Probability of the occurrence of a contingent event, and the probability of its non-occurrence, are opposite probabilities, the sum of the measures of which is unity. Suppose, as before, that one person is to be taken by lot from among five persons, A, B, C, D, and E. The Probability that the lot will fall on A is £, because he has one chance in five ; the probability that the lot mil not fall on A is £, because there are four chances mfive against its falling on A ; and the sum of £ and f is unity. (254.) The Probability of the non-occurrence of a contingent event, is the same thing as the improbability of that event; and is measured ...
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