This principle applies to a confirmation of expectation in an isolated instance, that A and B "will be associated in a fresh case." With regard to the desire for a general law in favor of A and B coexisting, the principle may be restated as follows: that the more A is found to be associated with B, "the more probable it is (if no cases of failure of association are known) that A is always associated with B." And a "sufficient number" of instances will make it almost "certain that A is always associated with B." If a general law is true, then particular cases must follow. Yet, particular cases may be true without the general law being true. Thus, the truth of a particular case is more probable than the truth of a general law.
It is important, finally, to understand the practice of induction relative to the appeal to experience, especially before moving on to the next chapter. One can imagine a man who had seen many white swans during his life and only white swans. Based on his data from his experience, he could argue that all swans are white. The fact that some are black is not an impediment to his argument because his account could be the case even though some information renders it improbable. The fact that this man's expectation (to only encounter white swans) might not be fulfilled does not mean that his "expectation will not probably be fulfilled in a given case or a given class of cases." Thus, an induction cannot be disproved by appealing to experience. It also cannot be proved by experience because experience cannot justify an induction with respect to future instances.
Arguments supported by experience assume the inductive principle. We must accept the inductive principle based on its "intrinsic evidence" or "forgo all justification of our expectations about the future." If we opt for the latter, then everyday expectations crumble: when what looks like a friend begins to walk toward us, then we can have no expectation that he is really our friend. We might as well believe him to be our worst enemy. General principles of science also depend on induction as we have seen. We believe in a principle like a law of motion because science has observed it to be a phenomenon without exception, many instances of its truth and none of its inaccuracy. We continue to believe that it will be true in the future only because we assume the inductive principle.
Russell makes an essential observation that knowledge about what is not experienced can be as fixed in its certainty in us as our knowledge from experience. Such is the power of a belief like induction, which experience can neither validate nor refute.