By good fortune.

synonyms: fortuitously, fortunately, luckily.

Roget 156: by chance, accidentally, by accident; casually; perchance etc. (possibly) 470; for aught one knows; as good would have it, as bad would have it, as luck would have it, as ill-luck would have it, as chance would have it; as it may be, as it may chance, as it may turn up, as it may happen; as the case may be.    ... show more