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An annuity payable during the life of the last survivor of two lives, for instance, will make a payment at the end of the year if either life survive; that is, if both lives survive, or if the first life surviwe and the other expire, or if the first life expire and the second surwive. The total probability, then, is the sum of these three separate probabilities.

No attempt will be made in this volume to develop these principles into mathematical formulas ; but the reader will not fail to find the foregoing principles both interesting and useful if he will give their statement in non-mathematical language careful attention.