Page:Chance, love, and logic - philosophical essays (IA chancelovelogicp00peir 0).pdf/119

 *sively. If we want the number of x's per y, and no x belongs to more than one y, we have only to divide the whole number of xs of ys by the number of y's. Such a method would, of course, fail if applied to finding the average number of street-car passengers per trip. We could not divide the total number of travelers by the number of trips, since many of them would have made many passages.

To find the probability that from a given class of premises, A, a given class of conclusions, B, follow, it is simply necessary to ascertain what proportion of the times in which premises of that class are true, the appropriate conclusions are also true. In other words, it is the number of cases of the occurrence of both the events A and B, divided by the total number of cases of the occurrence of the event A.

Addition of Relative Numbers.—Given two relative numbers having the same correlate, say the number of xs per y, and the number of zs per y; it is required to find the number of xs and zs together per y. If there is nothing which is at once an x and a z to the same y, the sum of the two given numbers would give the required number. Suppose, for example, that we had given the average number of friends that men have, and the average number of enemies, the sum of these two is the average number of persons interested in a man. On the other hand, it plainly would not do to add the average number of persons having constitutional diseases and over military age, to the average number exempted by each special cause from military service, in order to get the average number exempt in any way, since many are exempt in two or more ways at once.