This rule applies directly to probabilities, given the probability that two different and mutually exclusive events will happen under the same supposed set of circumstances. Given, for instance, the probability that if A then B, and also the probability that if A then C, then the sum of these two probabilities is the probability that if A then either B or C, so long as there is no event which belongs at once to the two classes B and C.
Rule III. Multiplication of Relative Numbers.—Suppose
that we have given the relative number of x's per y;
also the relative number of z's per x of y; or, to take a
concrete example, suppose that we have given, first, the
average number of children in families living in New York;
and, second, the average number of teeth in the head of a
New York child—then the product of these two numbers
would give the average number of children's teeth in a
New York family. But this mode of reckoning will only
apply in general under two restrictions. In the first place,
it would not be true if the same child could belong to different
families, for in that case those children who belonged
to several different families might have an exceptionally
large or small number of teeth, which would affect the
average number of children's teeth in a family more than
it would affect the average number of teeth in a child's head.
In the second place, the rule would not be true if different
children could share the same teeth, the average number
of children's teeth being in that case evidently something
different from the average number of teeth belonging to
a child.
