(1) We can make inferences by simple addition. If, for instance, there are two distinct properties observable in various members of the series, which properties do not occur in the same individual; it is plain that in any batch the number that are of one kind or the other will be equal to the sum of those of the two kinds separately. Thus 36.4 infants in 100 live to over sixty, 35.4 in 100 die before they are ten;[2] take a large number, say 10,000, then there will be about 3640 who live to over sixty, and about 3540 who do not reach ten; hence the total number who do not die within the assigned limits will be about 2820 altogether. Of course if these proportions were accurately assigned, the resultant sum would be equally accurate: but, as the reader knows, in Probability this proportion is merely the limit towards which the numbers tend in the long run, not the precise result assigned in any particular case. Hence we can only venture to say that this is the limit towards which we tend as the numbers become greater and greater. This rule, in its general algebraic form, would be expressed in the language of Probability as follows:--If the chances of two exclusive or incompatible events be respectively 1/m and 1/n the chance of one or other of them happening will be 1/m + 1/n or (m + n)/mn. Similarly if there were more than two events of the kind in question. On the principles adopted in this work, the rule, when thus algebraically expressed, means precisely the same thing as when it is expressed in the statistical form. It was shown at the conclusion of the last chapter that to say, for example, that the chance of a given event happening in a certain way is 1/6, is only another way of saying that in the long run it does tend to happen in that way once in six times. It is plain that a sort of corollary to this rule might be obtained, in precisely the same way, by subtraction instead of addition. Stated generally it would be as follows:--If the chance of one or other of two incompatible events be 1/m and the chance of one alone be 1/n, the chance of the remaining one will be 1/m - 1/n or (n - m)/nm. For example, if the chance of any one dying in a year is 1/10, and his chance of dying of some particular disease is 1/100, his chance of dying of any other disease is 9/100. The reader will remark here that there are two apparently different modes of stating this rule, according as we speak of 'one or other of two or more events happening,' or of 'the same event happening in one or other of two or more ways.' But no confusion need arise on this ground; either way of speaking is legitimate, the difference being merely verbal, and depending (as was shown in the first chapter, §8) upon whether the distinctions between the 'ways' are or are not too deep and numerous to entitle the event to be conventionally regarded as the same.