We may also here point out the justification for the common doctrine that certainty is represented by unity, just as any given degree of probability is represented by its appropriate fraction. If the statement that an event happens once in m times, is equivalently expressed by saying that its chance is 1/m, it follows that to say that it happens m times in m times, or every time without exception, is equivalent to saying that its chance is m/m or 1. Now an event that happens every time is of course one of whose occurrence we are certain; hence the fraction which represents the 'chance' of an event which is certain becomes unity. It will be equally obvious that given that the chance that an event will happen is 1/m, the chance that it will not happen is 1 - 1/m or (m - 1)/m. 3. (2) We can also make inferences by multiplication or division. Suppose that two events instead of being incompatible, are connected together in the sense that one is contingent upon the occurrence of the other. Let us be told that a given proportion of the members of the series possess a certain property, and a given proportion again of these possess another property, then the proportion of the whole which possess both properties will be found by multiplying together the two fractions which represent the above two proportions. Of the inhabitants of London, twenty-five in a thousand, say, will die in the course of the year; we suppose it to be known also that one death in five is due to fever; we should then infer that one in 200 of the inhabitants will die of fever in the course of the year. It would of course be equally simple, by division, to make a sort of converse inference. Given the total mortality per cent. of the population from fever, and the proportion of fever cases to the aggregate of other cases of mortality, we might have inferred, by dividing one fraction by the other, what was the total mortality per cent. from all causes. The rule as given above is variously expressed in the language of Probability. Perhaps the simplest and best statement is that it gives us the rule of dependent events. That is; if the chance of one event is 1/m, and the chance that if it happens another will also happen 1/n, then the chance of the latter is 1/mn. In this case it is assumed that the latter is so entirely dependent upon the former that though it does not always happen with it, it certainly will not happen without it; the necessity of this assumption however may be obviated by saying that what we are speaking of in the latter case is the _joint_ event, viz. both together if they are simultaneous events, or the latter _in consequence of_ the former, if they are successive.