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which contains one black and 35 white balls. If a black ball is drawn the first time and is not replaced, nothing but white can be drawn afterward; if a white ball is drawn the first time, and is not replaced, the chance of a black ball the next is not 1 :36 but r :35. But in either case, if the first ball is replaced, the chances remain the same, wiz., r:36, or a'6, for each trial.

The probabilities as to future events may be known in either of two ways, by- a priori reasoning or by knowledge of what has happened before under conditions precisely, similar. The deficiencies of the human mind are such that reasoning from the nature of things is perilous unless supported by experiment or observation. It is also in most matters very difficult to assure that past occurrences tool: place under conditions precisely similar to those which will hereafter obtain. Yet induction from the facts of experience in almost all things affords a safer basis for predictions of the future than does deduction from assumptions as to the nature of things, though the conditions be but approximately- and not exactly, the same.

The second most important principle of the science of probabilities, then, is that if out of a eery large number of trials, under conditions nearly, alike, an event has been observed to take place a certain number of times, then, under like conditions, the probabihty, that it will occur may be expressed by, a fraction of which the number of times it happened is the numerator and the number of trials—i. c. the number of times it happened plus the number of times it failed to happen—is the denominator. And the chance that it will not occur may be ex-pressed by a fraction with the same denominator, of