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1845. Whitworth's "Choice and Chance" is the most modern work and most nearly in text-book form.

The fundamental discovery was that certainty could be represented by unite and a chance by a fraction, the value of which can be computed, certain data being provided.

Thus suppose it were known that out of 36 persons on board a vessel, one had been lost, and there was nothing known to identify the person. Plainly it is an even chance, one with another, that a particular person was lost; and since there are 36 such equal chances, the chance as to any one person is in the ratio, 1 to 36, which is 3q. The chance that he was not the person lost is in the ratio, 35.36, which equals j Suppose that 6 were passengers and 30 were the crew; the chance that the person lost was a passenger is evidently 6 times as great as that he was a certain passenger. Now let the news be received that the person was a passenger, which then becomes a certainty. The chance that it was a particular passenger now becomes 11, i. C. one-sixth of unit}'; but that it was a passenger is six times as great, i. r., 6X1/6=i. That is, certainty is unity and all probabilities are fractions.

This reasoning is clear and conclusive as applied to past events. Now let us assume that it is known that out of 36 trials, a thing will happen once and fail to hap-pen 35 times. It is again evident that the chance of its happening is 1/36 and of its failing to happen is ; and this apphes to the first trial.

Whether it would apply to further trials or not would depend upon whether its happening is exclusive or not. For instance, suppose it is drawing balls from a box